testbookLayout.git

			@@ -1,25 +1,54 @@
			<template>
			<div class="chapter" num="5">

			<!-- 第四单元首页 -->
			<div class="page-box" page="120">
			<div v-if="showPageList.indexOf(120) > -1">
			<div class="padding-116">第四单元首页</div>
			<h1 id="a008">
			<img class="img-0" alt="" src="../../assets/images/dy4.jpg" />
			</h1>
			<div class="padding-116">
			<p>
			知识改变命运，技能成就人生，全社会坚持尊重劳动、尊重知识、尊重人才、尊重创造.著名厨师厉恩海曾是一名军人，练就了一身拉面绝活，他能把1
			kg
			的面拉出200多万根细如发丝的面条，4次创造吉尼斯世界纪录，被誉为“中国拉面大王”.拉面从一块面块开始，手握两端，两臂均匀用力加速向外抻拉，然后两头对折后再拉，每对折1次，面条的数量在原有基础上翻一倍，如此继续，每次对折后面条的数量形成下列数字1，2，4，8，16，32，64，…为了更好地体现面条数量与对折次数的关系，也可以表示为2<sup>0</sup>，2<sup>1</sup>，2<sup>2</sup>，2<sup>3</sup>，2<sup>4</sup>，2<sup>5</sup>，2<sup>6</sup>，…若用函数语言刻画这类数量关系和变化规律，就是我们即将学习的指数函数.现实生活中，数据量的爆炸式增长、细胞分裂、碳14考古、储蓄利率（复利）、血液中的酒精含量等问题，都会用到指数函数相关知识.
			</p>
			<p>
			指数函数与对数函数是两类基本初等函数，是提高数学运算能力、培养数形结合思想和数学建模能力的重要内容.它们在人口增长统计、文物考古鉴别、航海卫星定位等方面发挥着重要作用，在财经、金融、公共服务、信息技术等领域有广泛应用.
			</p>
			<p>
			本单元我们将在整数幂的基础上推广幂的概念，学习实数幂的相关定义和运算性质、指数函数的图像与性质、对数定义及运算法则、对数函数的图像与性质、指数函数与对数函数的实际应用等内容，感悟数学与现实的关联，把握事物的本质，形成理性思考问题的品质和精神.
			</p>
			</div>
			</div>
			</div>
			<!-- 目标 -->
			<div class="page-box" page="121">
			<div v-if="showPageList.indexOf(121) > -1">
			<div class="padding-116">目标</div>
			<div class="padding-116">
			<p class="left">
			<img class="inline2" alt="" src="../../assets/images/xxmb.jpg" />
			</p>
			<div class="fieldset">
			<p>1.实数指数幂.</p>
			<p>
			能体会指数从正整数推广到有理数、实数的过程，了解实数指数幂的运算法则.
			</p>
			<p>2.指数函数和对数函数.</p>
			<p>能借助几何直观和代数运算认识指数函数和对数函数；</p>
			<p>
			了解指数函数和对数函数的定义，理解它们的图像及性质，感悟数形结合的数学思想；
			</p>
			<p>会用对数的定义进行指数式与对数式的互化；</p>
			<p>了解对数的性质和运算法则.</p>
			<p>3.指数函数与对数函数的实际应用.</p>
			<p>能从实际情境抽象出指数函数、对数函数模型解决简单问题.</p>
			</div>
			</div>
			</div>
			</div>


			<!-- 115 -->
			<div class="page-box" page="122">
			<div v-if="showPageList.indexOf(122) > -1">


			<ul class="page-header-box">
			<li>
			<p>第四单元指数函数与对数函数</p>
			@@ -28,25 +57,886 @@
			<p><span>115</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<h2 id="b022">
			4.1 实数指数幂<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			</h2>
			<h3 id="c034">
			4.1.1 有理数指数幂<span class="fontsz2">＞＞＞</span>
			</h3>
			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/zshg.jpg" />
			</p>
			</div>
			<p class="block">
			如果<i>b</i><sup>2</sup>=<i>a</i>，那么<i>b</i>就叫作<i>a</i>
			的平方根（或二次方根）.因为<i>b</i><sup>2</sup>≥0，故当<i>a</i>＜0时，在实数范围内<i>a</i>没有平方根；当<i>a</i>＞0时，<i>a</i>的平方根有两个，它们互为相反数，分别为<math
			display="0">
			<msqrt>
			<mi>a</mi>
			</msqrt>
			</math>和<math display="0">
			<mo>−</mo>
			<msqrt>
			<mi>a</mi>
			</msqrt>
			</math>；当<i>a</i>=0时，
			<math display="0">
			<msqrt>
			<mn>0</mn>
			</msqrt>
			<mo>=</mo>
			<mn>0</mn>
			</math>.例如， ±3就是9的平方根.
			</p>
			<p class="block">
			如果<i>b</i><sup>3</sup>=<i>a</i>，那么<i>b</i>就叫作<i>a</i>的立方根（或三次方根）.在实数范围内<i>a</i>只有一个立方根，记为<math
			display="0">
			<mroot>
			<mi>a</mi>
			<mn>3</mn>
			</mroot>
			</math>.例如，2就是8的立方根.
			</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			一般地，如果<i>b<sup>n</sup></i>=<i>a</i>（<i>n</i>＞1，<i>n</i>∈<b>N</b>），那么<i>b</i>就叫作<i>a</i>的<i>n</i>次方根.
			</p>
			<p>
			当<i>n</i>是奇数时，正数<i>a</i>的<i>n</i>次方根是一个正数，负数<i>a</i>的<i>n</i>次方根是一个负数.这时，<i>a</i>的<i>n</i>次方根用符号<math
			display="0">
			<mroot>
			<mi>a</mi>
			<mi>n</mi>
			</mroot>
			</math>表示.例如，
			</p>
			<math display="block">
			<mroot>
			<mn>128</mn>
			<mn>7</mn>
			</mroot>
			<mo>=</mo>
			<mn>2</mn>
			<mo>，</mo>
			<mroot>
			<mrow>
			<mo>−</mo>
			<mn>128</mn>
			</mrow>
			<mn>7</mn>
			</mroot>
			<mo>=</mo>
			<mo>−</mo>
			<mn>2</mn>
			<mo>，</mo>
			<mroot>
			<msup>
			<mi>a</mi>
			<mrow>
			<mn>6</mn>
			</mrow>
			</msup>
			<mn>3</mn>
			</mroot>
			<mo>=</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo>.</mo>
			</math>
			<p>
			当<i>n</i>是偶数时，正数<i>a</i>的<i>n</i>次方根有两个，两数互为相反数.这时，正数<i>a</i>的正的<i>n</i>次方根用符号<math display="0">
			<mroot>
			<mi>a</mi>
			<mi>n</mi>
			</mroot>
			</math>表示，负的<i>n</i>次方根用符号<math display="0">
			<mo>−</mo>
			<mroot>
			<mi>a</mi>
			<mi>n</mi>
			</mroot>
			</math>表示.正的<i>n</i>次方根与负的<i>n</i>次方根可以合并写成<math display="0">
			<mo>±</mo>
			<mroot>
			<mi>a</mi>
			<mi>n</mi>
			</mroot>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mi>a</mi>
			<mo>＞</mo>
			<mn>0</mn>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>.例如，
			</p>
			<math display="block">
			<mroot>
			<mn>64</mn>
			<mn>6</mn>
			</mroot>
			<mo>=</mo>
			<mn>2</mn>
			<mo>,</mo>
			<mo>−</mo>
			<mroot>
			<mn>64</mn>
			<mn>6</mn>
			</mroot>
			<mo>=</mo>
			<mo>−</mo>
			<mn>2</mn>
			<mo>，</mo>
			<mo>±</mo>
			<mroot>
			<mn>64</mn>
			<mn>6</mn>
			</mroot>
			<mo>=</mo>
			<mo>±</mo>
			<mn>2.</mn>
			</math>
			<p>负数没有偶次方根.</p>
			<p>
			0的任何次方根都是0，记作
			<math display="0">
			<mroot>
			<mn>0</mn>
			<mi>n</mi>
			</mroot>
			<mo>=</mo>
			<mn>0</mn>
			</math>.
			</p>
			<p>
			形如
			<math display="0">
			<mroot>
			<mi>a</mi>
			<mi>n</mi>
			</mroot>
			<mo stretchy="false">(</mo>
			<mi>n</mi>
			<mo>＞</mo>
			<mn>1</mn>
			</math>（<i>n</i>＞1，<i>n</i>∈<b>N</b><sub>+</sub>）的式子叫作<b>根式</b>，<i>n</i>叫作<b>根指数</b>，<i>a</i>叫作<b>被开方数</b>.
			</p>
			<p>根据<i>n</i>次方根的定义，根式具有下列性质.</p>
			<p>
			（1）
			<math display="0">
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mroot>
			<mi>a</mi>
			<mi>n</mi>
			</mroot>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mi>n</mi>
			</mrow>
			</msup>
			<mo>=</mo>
			<mi>a</mi>
			</math>.
			</p>
			<p>
			（2）当<i>n</i>为奇数时，<math display="0">
			<mroot>
			<msup>
			<mi>a</mi>
			<mrow>
			<mi>n</mi>
			</mrow>
			</msup>
			<mi>n</mi>
			</mroot>
			<mo>=</mo>
			<mi>a</mi>
			</math>；
			</p>
			<p>
			当<i>n</i>为偶数时，<math display="0">
			<mroot>
			<msup>
			<mi>a</mi>
			<mrow>
			<mi>n</mi>
			</mrow>
			</msup>
			<mi>n</mi>
			</mroot>
			<mo>=</mo>
			<mrow>
			<mo stretchy="false">\|</mo>
			</mrow>
			<mi>a</mi>
			<mrow>
			<mo stretchy="false">\|</mo>
			</mrow>
			<mo>=</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">{</mo>
			<mtable columnalign="left left" columnspacing="1em" rowspacing="4pt">
			<mtr>
			<mtd>
			<mi>a</mi>
			<mo>,</mo>
			</mtd>
			<mtd>
			<mi>a</mi>
			<mo>⩾</mo>
			<mn>0</mn>
			<mo>，</mo>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mo>−</mo>
			<mi>a</mi>
			<mo>，</mo>
			</mtd>
			<mtd>
			<mi>a</mi>
			<mo>.</mo>
			<mo><</mo>
			<mn>0</mn>
			</mtd>
			</mtr>
			</mtable>
			<mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
			</mrow>
			</math>.
			</p>
			</div>
			</div>
			</div>
			<!-- 116 -->
			<div class="page-box" page="123">
			<div v-if="showPageList.indexOf(123) > -1">

			<ul class="page-header-odd fl al-end">
			<li>116</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p>
			<span class="zt-ls"><b>例1</b></span>　计算.
			</p>
			<p class="p-btn" >
			<span>（1）
			<math display="0">
			<mroot>
			<msup>
			<mn>5</mn>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mn>3</mn>
			</mroot>
			</math>；
			</span>
			<span class="btn-box" @click="isShowAnswer0 = !isShowAnswer0">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer0" >
			<span class="zt-ls"><b>解</b></span>（1）<math display="0">
			<mroot>
			<msup>
			<mn>5</mn>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mn>3</mn>
			</mroot>
			<mo>=</mo>
			<mn>5</mn>
			</math>；
			</p>
			<p class="p-btn" >
			<span>
			（2）
			<math display="0">
			<mroot>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mn>5</mn>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mn>3</mn>
			</mroot>
			</math>；
			</span>
			<span class="btn-box" @click="isShowAnswer1 = !isShowAnswer1">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer1" >
			<span class="zt-ls"><b>解</b></span>
			（2）
			<math display="0">
			<mroot>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mn>5</mn>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mn>3</mn>
			</mroot>
			<mo>=</mo>
			<mo>−</mo>
			<mn>5</mn>
			</math>；
			</p>
			<p class="p-btn" >
			<span>
			（3）
			<math display="0">
			<mroot>
			<msup>
			<mn>7</mn>
			<mrow>
			<mn>4</mn>
			</mrow>
			</msup>
			<mn>4</mn>
			</mroot>
			</math>；
			</span>
			<span class="btn-box" @click="isShowAnswer2 = !isShowAnswer2">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer2" >
			<span class="zt-ls"><b>解</b></span>
			（3）
			<math display="0">
			<mroot>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mn>7</mn>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>4</mn>
			</mrow>
			</msup>
			<mn>4</mn>
			</mroot>
			<mo>=</mo>
			<mn>7</mn>
			</math>；
			</p>
			<p class="p-btn" >
			<span>
			（4）
			<math display="0">
			<mroot>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mn>7</mn>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>4</mn>
			</mrow>
			</msup>
			<mn>4</mn>
			</mroot>
			</math>；
			</span>
			<span class="btn-box" @click="isShowAnswer3 = !isShowAnswer3">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer3" >
			<span class="zt-ls"><b>解</b></span>
			（4）
			<math display="0">
			<mroot>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mn>7</mn>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>4</mn>
			</mrow>
			</msup>
			<mn>4</mn>
			</mroot>
			<mo>=</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">\|</mo>
			<mo>−</mo>
			<mn>7</mn>
			<mo data-mjx-texclass="CLOSE">\|</mo>
			</mrow>
			<mo>=</mo>
			<mn>7</mn>
			</math>；
			</p>
			<p class="p-btn" >
			<span>（5） 81的4次方根.</span>
			<span class="btn-box" @click="isShowAnswer4 = !isShowAnswer4">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer4" >
			<span class="zt-ls"><b>解</b></span>
			（5）因为（±3）<sup>4</sup>=81，所以81的4次方根是±3，即<math display="0">
			<mo>±</mo>
			<mroot>
			<mn>81</mn>
			<mn>4</mn>
			</mroot>
			<mo>=</mo>
			<mo>±</mo>
			<mn>3</mn>
			</math>.
			</p>
			<p>
			<span class="zt-ls"><b>例2</b></span>　化简.
			</p>
			<p class="p-btn" >
			<span>
			（1）
			<math display="0">
			<mroot>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mn>3</mn>
			<mo>−</mo>
			<mi>a</mi>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mn>3</mn>
			</mroot>
			</math>；
			</span>
			<span class="btn-box" @click="isShowAnswer5 = !isShowAnswer5">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer5" >
			<span class="zt-ls"><b>解</b></span>（1）
			<math display="0">
			<mroot>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mn>3</mn>
			<mo>−</mo>
			<mi>a</mi>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mn>3</mn>
			</mroot>
			<mo>=</mo>
			<mn>3</mn>
			<mo>−</mo>
			<mi>a</mi>
			</math>；
			</p>
			<p class="p-btn" >
			<span>
			（2）
			<math display="0">
			<mroot>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mn>3</mn>
			<mo>−</mo>
			<mrow>
			<mi>π</mi>
			</mrow>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>4</mn>
			</mrow>
			</msup>
			<mn>4</mn>
			</mroot>
			</math>.
			</span>
			<span class="btn-box" @click="isShowAnswer6 = !isShowAnswer6">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer6" >
			<span class="zt-ls"><b>解</b></span>
			（2）
			<math display="0">
			<mroot>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mn>3</mn>
			<mo>−</mo>
			<mrow>
			<mi>π</mi>
			</mrow>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>4</mn>
			</mrow>
			</msup>
			<mn>4</mn>
			</mroot>
			<mo>=</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">\|</mo>
			<mn>3</mn>
			<mo>−</mo>
			<mrow>
			<mi>π</mi>
			</mrow>
			<mo data-mjx-texclass="CLOSE">\|</mo>
			</mrow>
			<mo>=</mo>
			<mo>−</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mn>3</mn>
			<mo>−</mo>
			<mrow>
			<mi>π</mi>
			</mrow>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mrow>
			<mi>π</mi>
			</mrow>
			<mo>−</mo>
			<mn>3</mn>
			</math>.
			</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			在初中，我们曾学习过整数幂的相关知识.<i>a<sup>n</sup></i>（<i>n</i>∈<b>N</b><sub>+</sub>）称为<i>a</i>的<i>n</i>次幂，<i>a</i>叫作底数，<i>n</i>叫作指数.
			</p>
			<p>
			（1）
			<math display="0">
			<msup>
			<mi>a</mi>
			<mrow>
			<mi>n</mi>
			</mrow>
			</msup>
			<mo>=</mo>
			<munder>
			<mrow data-mjx-texclass="OP">
			<munder>
			<mrow>
			<mi>a</mi>
			<mo>⋅</mo>
			<mi>a</mi>
			<mo>⋅</mo>
			<mi>a</mi>
			<mo>⋅</mo>
			<mo>⋯</mo>
			<mo>⋅</mo>
			<mi>a</mi>
			</mrow>
			<mo>⏟</mo>
			</munder>
			</mrow>
			<mrow>
			<mi>n</mi>
			<mo stretchy="false">↑</mo>
			<mi>a</mi>
			</mrow>
			</munder>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mi>n</mi>
			<mo>∈</mo>
			<msub>
			<mrow>
			<mi mathvariant="bold">N</mi>
			</mrow>
			<mrow>
			<mo>+</mo>
			</mrow>
			</msub>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>；
			</p>
			<p>（2） <i>a</i><sup>0</sup>=1（<i>a</i>≠0）；</p>
			<p>
			（3）
			<math display="0">
			<msup>
			<mi>a</mi>
			<mrow>
			<mo>−</mo>
			<mi>n</mi>
			</mrow>
			</msup>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<msup>
			<mi>a</mi>
			<mrow>
			<mi>n</mi>
			</mrow>
			</msup>
			</mfrac>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mi>a</mi>
			<mo>≠</mo>
			<mn>0</mn>
			<mo>,</mo>
			<mi>n</mi>
			<mo>∈</mo>
			<msub>
			<mrow>
			<mi mathvariant="bold">N</mi>
			</mrow>
			<mrow>
			<mo>+</mo>
			</mrow>
			</msub>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>.
			</p>
			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/gn.jpg" />
			</p>
			</div>
			<p class="block">分数指数幂</p>
			</div>
			<p>试想，如果幂指数<i>n</i>是分数时，此时的指数幂应该如何表示呢？</p>
			<p>
			为此，我们现将整数指数幂的概念进行推广，利用刚学习过的根式来表示分数指数幂，规定<b>分数指数幂</b>的意义如下（为简化讨论，我们约定底数<i>a</i>＞0）.
			</p>
			<math display="block">
			<mtable columnspacing="1em" rowspacing="4pt">
			<mtr>
			<mtd>
			<msup>
			<mi>a</mi>
			<mrow>
			<mfrac>
			<mi>m</mi>
			<mi>n</mi>
			</mfrac>
			</mrow>
			</msup>
			<mo>=</mo>
			<mroot>
			<msup>
			<mi>a</mi>
			<mrow>
			<mi>m</mi>
			</mrow>
			</msup>
			<mi>n</mi>
			</mroot>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mi>a</mi>
			<mo>></mo>
			<mn>0</mn>
			<mo>,</mo>
			<mi>m</mi>
			<mo>,</mo>
			<mi>n</mi>
			<mo>∈</mo>
			<msub>
			<mrow>
			<mi mathvariant="bold">N</mi>
			</mrow>
			<mrow>
			<mo>+</mo>
			</mrow>
			</msub>
			<mo>,</mo>
			<mi>n</mi>
			<mo>></mo>
			<mn>1</mn>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>,</mo>
			<mi>m</mi>
			<mo>=</mo>
			<mn>1</mn>
			<mtext> 时, 有 </mtext>
			<msup>
			<mi>a</mi>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mi>n</mi>
			</mfrac>
			</mrow>
			</msup>
			<mo>=</mo>
			<mroot>
			<mi>a</mi>
			<mi>n</mi>
			</mroot>
			<mo>.</mo>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<msup>
			<mi>a</mi>
			<mrow>
			<mo>−</mo>
			<mfrac>
			<mi>m</mi>
			<mi>n</mi>
			</mfrac>
			</mrow>
			</msup>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<msup>
			<mi>a</mi>
			<mrow>
			<mfrac>
			<mi>m</mi>
			<mi>n</mi>
			</mfrac>
			</mrow>
			</msup>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mroot>
			<msup>
			<mi>a</mi>
			<mrow>
			<mi>m</mi>
			</mrow>
			</msup>
			<mi>n</mi>
			</mroot>
			</mfrac>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mi>a</mi>
			<mo>></mo>
			<mn>0</mn>
			<mo>,</mo>
			<mi>m</mi>
			<mo>,</mo>
			<mi>n</mi>
			<mo>∈</mo>
			<msub>
			<mrow>
			<mi mathvariant="bold">N</mi>
			</mrow>
			<mrow>
			<mo>+</mo>
			</mrow>
			</msub>
			<mo>,</mo>
			<mi>n</mi>
			<mo>></mo>
			<mn>1</mn>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>.</mo>
			</mtd>
			</mtr>
			</mtable>
			</math>
			<p>
			这样，幂指数的概念就从整数指数幂推广到了有理数指数幂.只要每一个有理数指数幂有意义，整数指数幂的运算性质对有理数指数幂就同样适用.因此，我们初中
			</p>
			</div>
			</div>
			</div>
			<!-- 117 -->
			<div class="page-box" page="124">
			<div v-if="showPageList.indexOf(124) > -1">

			<ul class="page-header-box">
			<li>
			<p>第四单元指数函数与对数函数</p>
			@@ -55,7 +945,409 @@
			<p><span>117</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="t0">
			学习过的整数指数幂的运算性质就可以推广到有理数指数幂.
			</p>
			<p>设<i>a</i>＞0，<i>b</i>＞0，<i>m</i>，<i>n</i>∈<b>Q</b>，则</p>
			<p>
			（1） <i>a<sup>m</sup> a<sup>n</sup></i>=<i>a<sup>m+n</sup></i>；
			</p>
			<p>
			（2）（<i>a<sup>m</sup></i>）<i><sup>n</sup></i>=<i>a<sup>mn</sup></i>；
			</p>
			<p>
			（3）（<i>ab</i>）<i><sup>n</sup></i>=<i>a<sup>n</sup> b<sup>n</sup></i>.
			</p>
			<p>
			<span class="zt-ls"><b>例3</b></span>　将下列根式用分数指数幂表示（式中字母均为正实数）.
			</p>
			<p class="p-btn" >
			<span>
			（1）
			<math display="0">
			<mroot>
			<msup>
			<mi>a</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mn>4</mn>
			</mroot>
			</math>；
			</span>
			<span class="btn-box" @click="isShowAnswer7 = !isShowAnswer7">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer7" >
			<span class="zt-ls"><b>解</b></span>（1）
			<math display="0">
			<mroot>
			<msup>
			<mi>a</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mn>4</mn>
			</mroot>
			<mo>=</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mfrac>
			<mn>3</mn>
			<mn>4</mn>
			</mfrac>
			</mrow>
			</msup>
			</math>；
			</p>
			<p class="p-btn" >
			<span>
			（2）
			<math display="0">
			<mroot>
			<msup>
			<mi>x</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mn>6</mn>
			</mroot>
			</math>；
			</span>
			<span class="btn-box" @click="isShowAnswer8 = !isShowAnswer8">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer8" >
			<span class="zt-ls"><b>解</b></span>（2）
			<math display="0">
			<mroot>
			<msup>
			<mi>x</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mn>6</mn>
			</mroot>
			<mo>=</mo>
			<msup>
			<mi>x</mi>
			<mrow>
			<mfrac>
			<mn>2</mn>
			<mn>6</mn>
			</mfrac>
			</mrow>
			</msup>
			</math>；（注意：此处不能化简为<math display="0">
			<msup>
			<mi>x</mi>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			</math>）
			</p>
			<p class="p-btn" >
			<span>
			（3）
			<math display="0">
			<mfrac>
			<mn>1</mn>
			<mroot>
			<msup>
			<mn>5</mn>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mn>4</mn>
			</mroot>
			</mfrac>
			</math>.
			</span>
			<span class="btn-box" @click="isShowAnswer9 = !isShowAnswer9">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer9" >
			<span class="zt-ls"><b>解</b></span>（3）
			<math display="0">
			<mfrac>
			<mn>1</mn>
			<mroot>
			<msup>
			<mn>5</mn>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mn>4</mn>
			</mroot>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<msup>
			<mn>5</mn>
			<mrow>
			<mfrac>
			<mn>3</mn>
			<mn>4</mn>
			</mfrac>
			</mrow>
			</msup>
			</mfrac>
			<mo>=</mo>
			<msup>
			<mn>5</mn>
			<mrow>
			<mo>−</mo>
			<mfrac>
			<mn>3</mn>
			<mn>4</mn>
			</mfrac>
			</mrow>
			</msup>
			</math>
			</p>
			<p>
			<span class="zt-ls"><b>例4</b></span>　化简（式中字母均为正实数）.
			</p>
			<p class="p-btn" >
			<span>
			（1）<math display="0">
			<msup>
			<mn>27</mn>
			<mrow>
			<mo>−</mo>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			</math>；
			</span>
			<span class="btn-box" @click="isShowAnswer10 = !isShowAnswer10">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer10" >
			<span class="zt-ls"><b>解</b></span>（1）<math display="0">
			<msup>
			<mn>27</mn>
			<mrow>
			<mo>−</mo>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<msup>
			<mn>27</mn>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mroot>
			<mn>27</mn>
			<mn>3</mn>
			</mroot>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			</math>；
			</p>
			<p class="p-btn" >
			<span>
			（2）
			<math display="0">
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</mrow>
			</msup>
			<msup>
			<mi>b</mi>
			<mrow>
			<mo>−</mo>
			<mfrac>
			<mn>3</mn>
			<mn>4</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>8</mn>
			</mrow>
			</msup>
			</math>.
			</span>
			<span class="btn-box" @click="isShowAnswer11 = !isShowAnswer11">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer11" >
			<span class="zt-ls"><b>解</b></span>（2）<math display="0">
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</mrow>
			</msup>
			<msup>
			<mi>b</mi>
			<mrow>
			<mo>−</mo>
			<mfrac>
			<mn>3</mn>
			<mn>4</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>8</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>8</mn>
			</mrow>
			</msup>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mi>b</mi>
			<mrow>
			<mo>−</mo>
			<mfrac>
			<mn>3</mn>
			<mn>4</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>8</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mn>4</mn>
			</mrow>
			</msup>
			<msup>
			<mi>b</mi>
			<mrow>
			<mo>−</mo>
			<mn>6</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<mfrac>
			<msup>
			<mi>a</mi>
			<mrow>
			<mn>4</mn>
			</mrow>
			</msup>
			<msup>
			<mi>b</mi>
			<mrow>
			<mn>6</mn>
			</mrow>
			</msup>
			</mfrac>
			</math>.
			</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[124]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			</div>
			</div>
			</div>
			<!-- 118 -->
			@@ -66,41 +1358,1295 @@
			<li>数学.基础模块</li>
			<li>上册</li>
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			<div class="padding-116"></div>
			<div class="padding-116">
			<h3 id="c035">4.1.2 实数指数幂<span class="fontsz2">＞＞＞</span></h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/wttc.jpg" />
			</p>
			<p>
			小学我们学习了自然数，初中从自然数拓展到整数、有理数乃至实数.类似地，在学习有理数指数幂的基础上，我们可以将<i>a<sup>x</sup></i>中指数<i>x</i>的取值范围从有理数拓展到全体实数，此时，<i>a<sup>x</sup></i>的意义是什么呢？如<math
			display="0">
			<msup>
			<mn>2</mn>
			<mrow>
			<msqrt>
			<mn>3</mn>
			</msqrt>
			</mrow>
			</msup>
			</math>，<math display="0">
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>1</mn>
			<mn>4</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<msqrt>
			<mn>2</mn>
			</msqrt>
			</mrow>
			</msup>
			</math>，它们是一个确定的数吗？能否计算出结果呢？
			</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			实数指数幂事实上，我们可以通过科学计算器计算出<math display="0">
			<msup>
			<mn>2</mn>
			<mrow>
			<msqrt>
			<mn>3</mn>
			</msqrt>
			</mrow>
			</msup>
			</math>，<math display="0">
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>1</mn>
			<mn>4</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<msqrt>
			<mn>2</mn>
			</msqrt>
			</mrow>
			</msup>
			</math>的值（请同学们自己利用科学计算器或下载计算机软件进行计算）.如果精确到0.01时，<math display="0">
			<msup>
			<mn>2</mn>
			<mrow>
			<msqrt>
			<mn>3</mn>
			</msqrt>
			</mrow>
			</msup>
			</math>的近似值为3.32，<math display="0">
			<msup>
			<mfrac>
			<mn>1</mn>
			<mn>4</mn>
			</mfrac>
			<mrow>
			<msqrt>
			<mn>2</mn>
			</msqrt>
			</mrow>
			</msup>
			</math>的近似值为0.14，即表明这些无理数指数幂都是一个确定的实数.这样，我们将指数幂<i>a<sup>x</sup></i>（<i>a</i>＞0）中指数<i>x</i>的取值范围从整数逐步拓展到有理数、无理数，乃至实数.当<i>x</i>为任意实数时，<b>实数指数幂</b><i>a<sup>x</sup></i>（<i>a</i>＞0）表示一个确定实数.现实生活中，我们通过类比、联想、猜想等方式可创新设计出很多不同的事物和模式.
			</p>
			<p>
			有理数指数幂的运算性质同样适用于实数指数幂的运算性质（证明略），即当<i>a</i>＞0，<i>b</i>＞0，<i>p</i>，<i>q</i>∈<b>R</b>时，有
			</p>
			<p>
			（1） <i>a<sup>p</sup> a<sup>q</sup></i>=<i>a<sup>p+q</sup></i>；
			</p>
			<p>
			（2）（<i>a<sup>p</sup></i>）<i><sup>q</sup></i>=<i>a<sup>pq</sup></i>；
			</p>
			<p>
			（3）（<i>ab</i>）<i><sup>p</sup></i>=<i>a<sup>p</sup> b<sup>p</sup></i>.
			</p>
			<p>注意：运算性质成立的条件是每个实数指数幂都有意义.</p>
			</div>
			</div>
			</div>
			<!-- 119 -->
			<div class="page-box" page="126">
			<div v-if="showPageList.indexOf(126) > -1">

			<ul class="page-header-box">
			<li>
			<p>第四单元指数函数与对数函数</p>
			</li>
			<li>
			<p><span>119</span></p>
			<p><span>119-120</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" />
			</p>
			</div>
			<p class="block">
			对例1（1）
			题，我们需要将某些底数变形为指数幂的形式，以方便利用实数指数幂的运算法则进行计算或者化简.
			</p>
			</div>
			<p>
			<span class="zt-ls"><b>例1</b></span>　计算（式中字母均为正实数）.
			</p>
			<p class="p-btn" >
			<span>
			（1）<math display="0">
			<msup>
			<mn>16</mn>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>4</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>−</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mfrac>
			<mn>1</mn>
			<mn>27</mn>
			</mfrac>
			<mrow>
			<mo>−</mo>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>+</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">（</mo>
			<msqrt>
			<mn>2</mn>
			</msqrt>
			<mo>−</mo>
			<mn>1</mn>
			<mo data-mjx-texclass="CLOSE">）</mo>
			</mrow>
			<mrow>
			<mn>0</mn>
			</mrow>
			</msup>
			</math>；
			</span>
			<span class="btn-box" @click="isShowAnswer12 = !isShowAnswer12">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer12" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			</p>
			<p class="left1">
			<math display="">
			<mtable columnalign="left" columnspacing="1em" rowspacing="4pt">
			<mtr>
			<mtd>
			<mtext>（1）</mtext>
			<msup>
			<mn>16</mn>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>4</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>−</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>1</mn>
			<mn>27</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mo>−</mo>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>+</mo>
			<mo stretchy="false">(</mo>
			<msqrt>
			<mn>2</mn>
			</msqrt>
			<mo>−</mo>
			<mn>1</mn>
			<msup>
			<mo stretchy="false">)</mo>
			<mrow>
			<mn>0</mn>
			</mrow>
			</msup>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mo>=</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>4</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>4</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>−</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">[</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">]</mo>
			</mrow>
			<mrow>
			<mo>−</mo>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>+</mo>
			<mn>1</mn>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mo>=</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>4</mn>
			<mo>×</mo>
			<mfrac>
			<mn>1</mn>
			<mn>4</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>−</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>3</mn>
			<mo>×</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</mrow>
			</msup>
			<mo>+</mo>
			<mn>1</mn>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mo>=</mo>
			<mn>2</mn>
			<mo>−</mo>
			<mn>3</mn>
			<mo>+</mo>
			<mn>1</mn>
			<mo>=</mo>
			<mn>0</mn>
			<mo>;</mo>
			</mtd>
			</mtr>
			</mtable>
			</math>
			</p>
			</div>
			<p class="p-btn" >
			<span>
			（2）
			<math display="0">
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mo>−</mo>
			<mn>3</mn>
			</mrow>
			</msup>
			<msup>
			<mi>b</mi>
			<mrow>
			<mn>5</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>5</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>⋅</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>5</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>÷</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<msup>
			<mi>b</mi>
			<mrow>
			<mfrac>
			<mn>5</mn>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mfrac>
			<mn>3</mn>
			<mn>5</mn>
			</mfrac>
			</mrow>
			</msup>
			</math>.
			</span>
			<span class="btn-box" @click="isShowAnswer13 = !isShowAnswer13">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer13" class="left1">
			<math display="">
			<mtable columnalign="left" columnspacing="1em" rowspacing="4pt">
			<mtr>
			<mtd>
			<mtext>（2）</mtext>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mo>−</mo>
			<mn>3</mn>
			</mrow>
			</msup>
			<msup>
			<mi>b</mi>
			<mrow>
			<mn>5</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>5</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>⋅</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>5</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>÷</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<msup>
			<mi>b</mi>
			<mrow>
			<mfrac>
			<mn>5</mn>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mfrac>
			<mn>3</mn>
			<mn>5</mn>
			</mfrac>
			</mrow>
			</msup>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mo>=</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mo>−</mo>
			<mn>3</mn>
			<mo>×</mo>
			<mfrac>
			<mn>1</mn>
			<mn>5</mn>
			</mfrac>
			</mrow>
			</msup>
			<msup>
			<mi>b</mi>
			<mrow>
			<mn>5</mn>
			<mo>×</mo>
			<mfrac>
			<mn>1</mn>
			<mn>5</mn>
			</mfrac>
			</mrow>
			</msup>
			<msup>
			<mi>a</mi>
			<mrow>
			<mn>2</mn>
			<mo>×</mo>
			<mfrac>
			<mn>1</mn>
			<mn>5</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>÷</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mn>3</mn>
			<mo>×</mo>
			<mfrac>
			<mn>3</mn>
			<mn>5</mn>
			</mfrac>
			</mrow>
			</msup>
			<msup>
			<mi>b</mi>
			<mrow>
			<mfrac>
			<mn>5</mn>
			<mn>3</mn>
			</mfrac>
			<mo>×</mo>
			<mfrac>
			<mn>3</mn>
			<mn>5</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mo>=</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mo>−</mo>
			<mfrac>
			<mn>3</mn>
			<mn>5</mn>
			</mfrac>
			<mo>+</mo>
			<mfrac>
			<mn>2</mn>
			<mn>5</mn>
			</mfrac>
			<mo>−</mo>
			<mfrac>
			<mn>9</mn>
			<mn>5</mn>
			</mfrac>
			</mrow>
			</msup>
			<msup>
			<mi>b</mi>
			<mrow>
			<mn>1</mn>
			<mo>−</mo>
			<mn>1</mn>
			</mrow>
			</msup>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mo>=</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mo>−</mo>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<msup>
			<mi>a</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			</mfrac>
			<mo>.</mo>
			</mtd>
			</mtr>
			</mtable>
			</math>
			</p>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例2</b></span>　化简（式中字母均为正实数）.
			</span>
			<span class="btn-box" @click="openDialog(thinkOne)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
			<path class="a"
			d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
			transform="translate(-3761 14334.001)" />
			</svg>
			</span>
			</p>
			<p class="p-btn" >
			<span>
			（1）
			<math display="0">
			<msqrt>
			<mn>2</mn>
			</msqrt>
			<mo>×</mo>
			<mroot>
			<mn>8</mn>
			<mn>4</mn>
			</mroot>
			<mo>×</mo>
			<mroot>
			<mn>64</mn>
			<mn>8</mn>
			</mroot>
			</math>；
			</span>
			<span class="btn-box" @click="isShowAnswer14 = !isShowAnswer14">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer14" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			</p>
			<math display="">
			<mtable columnalign="left" columnspacing="1em" rowspacing="4pt">
			<mtr>
			<mtd>
			<mo stretchy="false">（1）</mo>
			<msqrt>
			<mn>2</mn>
			</msqrt>
			<mo>×</mo>
			<mroot>
			<mn>8</mn>
			<mn>4</mn>
			</mroot>
			<mo>×</mo>
			<mroot>
			<mn>64</mn>
			<mn>8</mn>
			</mroot>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mo>=</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>×</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>4</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>×</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>6</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>8</mn>
			</mfrac>
			</mrow>
			</msup>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mo>=</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>×</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mfrac>
			<mn>3</mn>
			<mn>4</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>×</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mfrac>
			<mn>6</mn>
			<mn>8</mn>
			</mfrac>
			</mrow>
			</msup>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mo>=</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mo>+</mo>
			<mfrac>
			<mn>3</mn>
			<mn>4</mn>
			</mfrac>
			<mo>+</mo>
			<mfrac>
			<mn>6</mn>
			<mn>8</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>=</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<mn>4</mn>
			<mo>;</mo>
			</mtd>
			</mtr>
			</mtable>
			</math>
			</div>
			<p class="p-btn" >
			<span>
			（2）
			<math display="0">
			<msqrt>
			<msup>
			<mi>a</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<msup>
			<mi>b</mi>
			<mrow>
			<mo>−</mo>
			<mn>3</mn>
			</mrow>
			</msup>
			</msqrt>
			<mo>·</mo>
			<mroot>
			<mrow>
			<msup>
			<mi>a</mi>
			<mrow>
			<mo>−</mo>
			<mn>2</mn>
			</mrow>
			</msup>
			<msup>
			<mi>b</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			</mrow>
			<mn>3</mn>
			</mroot>
			<mo>·</mo>
			<mroot>
			<mrow>
			<mi>a</mi>
			<msup>
			<mi>b</mi>
			<mrow>
			<mn>5</mn>
			</mrow>
			</msup>
			</mrow>
			<mn>6</mn>
			</mroot>
			</math>.
			</span>
			<span class="btn-box" @click="isShowAnswer15 = !isShowAnswer15">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<math v-if="isShowAnswer15" display="">
			<mtable columnalign="left" columnspacing="1em" rowspacing="4pt">
			<mtr>
			<mtd>
			<mtext>（2）</mtext>
			<msqrt>
			<msup>
			<mi>a</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<msup>
			<mi>b</mi>
			<mrow>
			<mo>−</mo>
			<mn>3</mn>
			</mrow>
			</msup>
			</msqrt>
			<mo>⋅</mo>
			<mroot>
			<mrow>
			<msup>
			<mi>a</mi>
			<mrow>
			<mo>−</mo>
			<mn>2</mn>
			</mrow>
			</msup>
			<msup>
			<mi>b</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			</mrow>
			<mn>3</mn>
			</mroot>
			<mo>⋅</mo>
			<mroot>
			<mrow>
			<mi>a</mi>
			<msup>
			<mi>b</mi>
			<mrow>
			<mn>5</mn>
			</mrow>
			</msup>
			</mrow>
			<mn>6</mn>
			</mroot>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mo>=</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<msup>
			<mi>b</mi>
			<mrow>
			<mo>−</mo>
			<mn>3</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>⋅</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mo>−</mo>
			<mn>2</mn>
			</mrow>
			</msup>
			<msup>
			<mi>b</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>⋅</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mi>a</mi>
			<msup>
			<mi>b</mi>
			<mrow>
			<mn>5</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>6</mn>
			</mfrac>
			</mrow>
			</msup>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mo>=</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mfrac>
			<mn>3</mn>
			<mn>2</mn>
			</mfrac>
			</mrow>
			</msup>
			<msup>
			<mi>b</mi>
			<mrow>
			<mo>−</mo>
			<mfrac>
			<mn>3</mn>
			<mn>2</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>⋅</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mo>−</mo>
			<mfrac>
			<mn>2</mn>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			<msup>
			<mi>b</mi>
			<mrow>
			<mfrac>
			<mn>2</mn>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>⋅</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>6</mn>
			</mfrac>
			</mrow>
			</msup>
			<msup>
			<mi>b</mi>
			<mrow>
			<mfrac>
			<mn>5</mn>
			<mn>6</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mo>=</mo>
			<msup>
			<mi>a</mi>
			<mrow>
			<mfrac>
			<mn>3</mn>
			<mn>2</mn>
			</mfrac>
			<mo>−</mo>
			<mfrac>
			<mn>2</mn>
			<mn>3</mn>
			</mfrac>
			<mo>+</mo>
			<mfrac>
			<mn>1</mn>
			<mn>6</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>⋅</mo>
			<msup>
			<mi>b</mi>
			<mrow>
			<mo>−</mo>
			<mfrac>
			<mn>3</mn>
			<mn>2</mn>
			</mfrac>
			<mo>+</mo>
			<mfrac>
			<mn>2</mn>
			<mn>3</mn>
			</mfrac>
			<mo>+</mo>
			<mfrac>
			<mn>5</mn>
			<mn>6</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>=</mo>
			<mi>a</mi>
			<mo>.</mo>
			</mtd>
			</mtr>
			</mtable>
			</math>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例3</b></span>　计算
			2<sup>0</sup>+2<sup>1</sup>+2<sup>2</sup>+2<sup>3</sup>+…+2<i><sup>x</sup></i>（<i>x</i>∈<b>N</b>）.
			</span>
			<span class="btn-box" @click="isShowAnswer16 = !isShowAnswer16">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			<span class="btn-box" @click="openDialog(thinkTwo)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
			<path class="a"
			d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
			transform="translate(-3761 14334.001)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer16" >
			<p>
			<span class="zt-ls"><b>解</b></span> 令
			</p>
			<math display="block">
			<mi>S</mi>
			<mo>=</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>0</mn>
			</mrow>
			</msup>
			<mo>+</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>1</mn>
			</mrow>
			</msup>
			<mo>+</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo>+</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mo>+</mo>
			<mo>…</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mi>x</mi>
			<mo>−</mo>
			<mn>1</mn>
			</mrow>
			</msup>
			<mo>+</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mi>x</mi>
			</mrow>
			</msup>
			<mo>.</mo>
			</math>
			<p class="right">①</p>
			<p>将①式两边同时乘2，得</p>
			<math display="block">
			<mn>2</mn>
			<mi>S</mi>
			<mo>=</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>1</mn>
			</mrow>
			</msup>
			<mo>+</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo>+</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mo>+</mo>
			<mo>…</mo>
			<mo>+</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mi>x</mi>
			</mrow>
			</msup>
			<mo>+</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mi>x</mi>
			<mo>+</mo>
			<mn>1</mn>
			</mrow>
			</msup>
			<mo>.</mo>
			</math>
			<p class="right">②</p>
			<p>用②式减①式可得</p>
			<p>
			2<i>S</i>-<i>S</i>=（2<sup>1</sup>+2<sup>2</sup>+2<sup>3</sup>+…+2<i><sup>x</sup></i>+2<i><sup>x</sup></i><sup>+1</sup>）-（2<sup>0</sup>+2<sup>1</sup>+2<sup>2</sup>+2<sup>3</sup>+…+2<i><sup>x</sup></i><sup>-1</sup>+2<i><sup>x</sup></i>），
			</p>
			<p>
			即<i>S</i>=2<i><sup>x+1</sup></i>-1，
			</p>
			<p>
			所以，　2<sup>0</sup>+2<sup>1</sup>+2<sup>2</sup>+2<sup>3</sup>+…+2<i><sup>x</sup></i>=2<i><sup>x+1</sup></i>-1.
			</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[127]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			</div>
			</div>
			</div>
			<!-- 120 -->
			<div class="page-box" page="127">
			<div v-if="showPageList.indexOf(127) > -1">

			<ul class="page-header-odd fl al-end">
			<li>120</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			</div>
			<div class="page-box hidePage" page="127">
			</div>
			<!-- 121 -->
			<div class="page-box" page="128">
			<div v-if="showPageList.indexOf(128) > -1">

			<ul class="page-header-box">
			<li>
			<p>第四单元指数函数与对数函数</p>
			@@ -109,7 +2655,76 @@
			<p><span>121</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<h3 id="c036">习题4.1<span class="fontsz2">＞＞＞</span></h3>
			<div class="bj">
			<examinations :cardList="questionData[128]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			<h2 id="b023">
			4.2 指数函数<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			</h2>
			<h3 id="c037">
			4.2.1 指数函数的定义与图像<span class="fontsz2">＞＞＞</span>
			</h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/gcsk.jpg" />
			</p>
			<p>
			情境1：《庄子·天下篇》中有一段脍炙人口的话：“一尺之棰，日取其半，万世不竭.”这里的“一尺之棰”，即一尺（长度单位，1尺约合0.33
			m）长的木棍，“日取其半”即每天取它的一半.若一直“日取其半”，则每天剩下的木棍长度就是下面的一列数字.
			</p>
			<math display="block">
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mo>,</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo>,</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mo>,</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>4</mn>
			</mrow>
			</msup>
			<mo>,</mo>
			<mo>⋯</mo>
			</math>
			</div>
			</div>
			</div>
			<!-- 122 -->
			@@ -120,13 +2735,214 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p>
			记取到第<i>x</i>天时剩下的长度为<i>y</i>，那么<i>y</i>与
			<i>x</i>的函数关系是
			</p>
			<math display="block">
			<mi>y</mi>
			<mo>=</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mi>x</mi>
			</mrow>
			</msup>
			<mo>.</mo>
			</math>
			<p class="right">①</p>
			<p>
			其中指数<i>x</i>是自变量，定义域是<i>x</i>∈<b>N</b><sub>+</sub>.
			</p>
			<p>
			情境2：细胞每分裂1次其数量变为原来的两倍，则每次分裂后的细胞数量见表4-1.
			</p>
			<p class="img">表4-1</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0133-2.jpg" />
			</p>
			<p>
			如果设细胞分裂的次数为<i>x</i>，对应分裂后的细胞数量为<i>y</i>，那么<i>y</i>与<i>x</i>的函数关系是
			</p>
			<math display="block">
			<mi>y</mi>
			<mo>=</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mn>2</mn>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mi>x</mi>
			</mrow>
			</msup>
			<mo>.</mo>
			</math>
			<p class="right">②</p>
			<p>
			其中指数<i>x</i>是自变量，定义域是<i>x</i>∈<b>N</b><sub>+</sub>.
			</p>
			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/gn.jpg" />
			</p>
			</div>
			<p class="block">指数函数</p>
			</div>
			<p>
			如果用字母<i>a</i>代替上述①②两式中的底数<math display="0">
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</math>和2，那么函数<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mi>x</mi>
			</mrow>
			</msup>
			</math>和 <i>y</i>=2<i><sup>x</sup></i>就可以表示为
			</p>
			<p class="center">
			<i>y</i>=<i>a<sup>x</sup></i>
			</p>
			<p>
			的形式，其中指数<i>x</i>是自变量，底数<i>a</i>是一个大于0且不等于
			1的常量.
			</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			一般地，形如<i>y</i>=<i>a<sup>x</sup></i>（<i>a</i>＞0，且<i>a</i>≠1）的函数叫作<b>指数函数</b>，其中指数<i>x</i>是自变量，定义域是<b>R</b>.
			</p>
			<p>
			<b>例</b> 已知指数函数<i>f</i>（<i>x</i>）=<i>a<sup>x</sup></i>（<i>a</i>＞0，且<i>a</i>≠1），且<i>f</i>（3）=125.
			</p>
			<p class="p-btn" >
			<span>
			（1）求函数<i>f</i>（<i>x</i>）的解析式；
			</span>
			<span class="btn-box" @click="isShowAnswer17 = !isShowAnswer17">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer17" >
			<span class="zt-ls"><b>解</b></span>（1）
			因为<i>f</i>（<i>x</i>）=<i>a<sup>x</sup></i>（<i>a</i>＞0，且<i>a</i>≠1），且<i>f</i>（3）=125，所以<i>a</i><sup>3</sup>=125，解得<i>a</i>=5，于是<i>f</i>（<i>x</i>）=5<i><sup>x</sup></i>.
			</p>
			<p class="p-btn" >
			<span>
			（2）求<i>f</i>（0），<i>f</i>（2），<i>f</i>（-2），<math display="0">
			<mi>f</mi>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>的值.
			</span>
			<span class="btn-box" @click="isShowAnswer18 = !isShowAnswer18">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer18">
			<span class="zt-ls"><b>解</b></span>（2）
			<i>f</i>（0）=5<sup>0</sup>=1，<i>f</i>（2）=5<sup>2</sup>=25，<math display="0">
			<mi>f</mi>
			<mo>−</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mn>2</mn>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<msup>
			<mn>5</mn>
			<mrow>
			<mo>−</mo>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<msup>
			<mn>5</mn>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>25</mn>
			</mfrac>
			</math>，<math display="0">
			<mi>f</mi>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<msup>
			<mn>5</mn>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>=</mo>
			<msqrt>
			<mn>5</mn>
			</msqrt>
			</math>.
			</p>
			</div>
			</div>
			</div>
			<!-- 123 -->
			<div class="page-box" page="130">
			<div v-if="showPageList.indexOf(130) > -1">

			<ul class="page-header-box">
			<li>
			<p>第四单元指数函数与对数函数</p>
			@@ -135,7 +2951,78 @@
			<p><span>123</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<div class="bk-hzjl">
			<div class="bj1-hzjl">
			<p class="left">
			<img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
			</p>
			</div>
			<examinations :cardList="questionData[130]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/zshg.jpg" />
			</p>
			</div>
			<p class="block">
			初中我们学习了正比例函数、反比例函数和二次函数，通过描点法画出它们的图像分别是直线、双曲线和抛物线（如图4-1所示）.我们可类比借鉴学习上述函数的经验，画出指数函数的图像，再利用图像与解析式，研究其单调性、奇偶性等.
			</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0134-3.jpg" />
			</p>
			<p class="img">图4-1</p>
			</div>
			<p><b>类比归纳</b></p>
			<p>
			与初中画二次函数图像一样，也可用描点法画出指数函数的图像.下面我们以<i>y</i>=2<i><sup>x</sup></i>和<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mi>x</mi>
			</mrow>
			</msup>
			</math>为例，画出其函数图像.
			</p>
			<p>第一步：列表（如表4-2所示）.</p>
			<p class="img">表4-2</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0134-5.jpg" />
			</p>
			<p>
			第二步：描点，并且用光滑的曲线连接所描的点，画出它们的图像（如图4-2所示）.
			</p>
			<p>
			利用相同方法，我们还可以在同一平面直角坐标系中画出<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>2</mn>
			<mn>5</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mi>x</mi>
			</mrow>
			</msup>
			</math>，
			</p>
			</div>
			</div>
			</div>
			<!-- 124 -->
			@@ -146,14 +3033,127 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mi>x</mi>
			</mrow>
			</msup>
			</math>， <i>y</i>=2.3<i><sup>x</sup></i>，<i>y</i>=3<i><sup>x</sup></i>的图像，如图4-3所示.
			<ul class="fl">
			<li style="margin-top: 30px">
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0135-2.jpg" />
			</p>
			<p class="img">图4-2</p>
			</li>
			<li>
			<p class="center">
			<img class="img-b" alt="" src="../../assets/images/0135-3.jpg" />
			</p>
			<p class="img">图4-3</p>
			</li>
			</ul>
			<h3 id="c038">
			4.2.2 指数函数的性质<span class="fontsz2">＞＞＞</span>
			</h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/gcsk.jpg" />
			</p>
			<p>
			观察指数函数的图像，描述这些图像在位置、公共点和变化趋势等方面的共性特征.
			</p>
			<p>
			（1）图中所有指数函数图像均在<i>x</i>轴的上方（<b>位置特征</b>）；
			</p>
			<p>
			（2）图中所有指数函数图像都经过定点（0，1）（<b>公共点特征</b>）；
			</p>
			<p>
			（3）
			在定义域内，指数函数<i>y</i>=2<i><sup>x</sup></i>，<i>y</i>=2.3<i><sup>x</sup></i>，<i>y</i>=3<i><sup>x</sup></i>图像从左向右分别逐渐上升，在第二象限内向左与<i>x</i>轴无限接近；指数函数<math
			display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mi>x</mi>
			</mrow>
			</msup>
			</math>，<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>2</mn>
			<mn>5</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mi>x</mi>
			</mrow>
			</msup>
			</math>，<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mi>x</mi>
			</mrow>
			</msup>
			</math>图像从左向右分别逐渐下降，在第一象限内向右与<i>x</i>轴无限接近（<b>变化趋势特征</b>）.
			</p>
			<p>
			我们观察分析发现，指数函数<i>y</i>=<i>a<sup>x</sup></i>（<i>a</i>＞0，且<i>a</i>≠1）的图像按底数<i>a</i>的取值，可分为0＜<i>a</i>＜1和<i>a</i>＞1两种类型.
			</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			一般地，指数函数<i>y</i>=<i>a<sup>x</sup></i>（<i>a</i>＞0，且<i>a</i>≠1）具有下列性质.
			</p>
			<p>（1）函数的定义域为<i>R</i>，值域为（0，+∞）；</p>
			<p>（2）当<i>x</i>=0时，函数值<i>y</i>=1；</p>
			<p>
			（3）
			当<i>a</i>＞1时，函数在（-∞，+∞）内是增函数；当0＜<i>a</i>＜1时，函数在（-∞，+∞）内是减函数.
			</p>
			</div>
			</div>
			</div>
			<!-- 125 -->
			<div class="page-box" page="132">
			<div v-if="showPageList.indexOf(132) > -1">


			<ul class="page-header-box">
			<li>
			<p>第四单元指数函数与对数函数</p>
			@@ -162,37 +3162,430 @@
			<p><span>125</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p>
			指数函数<i>y</i>=<i>a<sup>x</sup></i>（<i>a</i>＞0，且<i>a</i>≠1）的图像和性质可以总结如表4-3所示.
			</p>
			<p class="img">表4-3</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0136-1.jpg" />
			</p>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例1</b></span>　判断下列函数哪些是指数函数，并画出函数图像验证.
			</span>
			<span class="btn-box" @click="isShowAnswer19 = !isShowAnswer19">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p>
			（1） <i>y</i>=0.5<i><sup>x</sup></i>；（2） <i>y</i>=2×3<i><sup>x</sup></i>；（3） <i>y</i>=<i>x</i><sup>2</sup>.
			</p>
			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" />
			</p>
			</div>
			<p class="block">
			函数<i>y</i>=2×3<i><sup>x</sup></i>
			</p>
			<p class="block">
			在形式上与指数函数相似，但不符合指数函数的定义，我们从其函数图像可以看到没有过定点（0，1）.
			</p>
			</div>
			<div v-if="isShowAnswer19" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			依据指数函数<i>y</i>=<i>a<sup>x</sup></i>的定义，<i>y</i>=0.5<i><sup>x</sup></i>是指数函数，<i>y</i>=2×3<i><sup>x</sup></i>和<i>y</i>=<i>x</i><sup>2</sup>不是指数函数.画出函数图像（如图4-4所示），函数<i>y</i>=0.5<i><sup>x</sup></i>的图像符合指数函数图像的特征；函数<i>y</i>=2×3<i><sup>x</sup></i>的图像虽与指数函数图像很相似，但并没有过定点（0，1）；函数<i>y</i>=<i>x</i><sup>2</sup>的图像是二次函数的图像.
			</p>
			<p class="center">
			<img class="img-b" alt="" src="../../assets/images/0136-2.jpg" />
			</p>
			<p class="img">图4-4</p>
			</div>
			<iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
			<div class="bk-hzjl">
			<div class="bj1-hzjl">
			<p class="left">
			<img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
			</p>
			</div>
			<examinations :cardList="questionData[131]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			</div>
			</div>
			</div>
			<!-- 126 -->
			<div class="page-box" page="133">
			<div v-if="showPageList.indexOf(133) > -1">
			<ul class="page-header-odd fl al-end">
			<li>126</li>
			<li>126-127</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p>
			<span class="zt-ls"><b>例2</b></span>　判断下列函数在（-∞，+∞）内的单调性.
			</p>
			<p class="p-btn" >
			<span>（1） <i>y</i>=4<i><sup>x</sup></i>；</span>
			<span class="btn-box" @click="isShowAnswer20 = !isShowAnswer20">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer20" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）因为4＞1 ，所以<i>y</i>=4<i><sup>x</sup></i>在（-∞，+∞）内是增函数（如图4-5所示）.
			</p>
			<p class="center">
			<img class="img-f" alt="" src="../../assets/images/0137-7.jpg" />
			</p>
			<p class="img">图4-5</p>
			</div>
			<p class="p-btn" >
			<span>（2） <i>y</i>=3<i><sup>-x</sup></i>；</span>
			<span class="btn-box" @click="isShowAnswer21 = !isShowAnswer21">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer21" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			（2）
			<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msup>
			<mn>3</mn>
			<mrow>
			<mo>−</mo>
			<mi>x</mi>
			</mrow>
			</msup>
			<mo>=</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mn>3</mn>
			<mrow>
			<mo>−</mo>
			<mn>1</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mi>x</mi>
			</mrow>
			</msup>
			<mo>=</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mi>x</mi>
			</mrow>
			</msup>
			</math>，因为<math display="0">
			<mn>0</mn>
			<mo>＜</mo>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			<mo>＜</mo>
			<mn>1</mn>
			</math>，所以<i>y</i>=3<i><sup>-x</sup></i>在（-∞，+∞）内是减函数（如图4-6所示）.
			</p>
			<p class="center">
			<img class="img-f" alt="" src="../../assets/images/0137-8.jpg" />
			</p>
			<p class="img">图4-6</p>
			</div>
			<p class="p-btn" >
			<span>
			（3）
			<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mfrac>
			<mi>x</mi>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			</math>.
			</span>
			<span class="btn-box" @click="isShowAnswer22 = !isShowAnswer22">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer22" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			（3）<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mfrac>
			<mi>x</mi>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>=</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mi>x</mi>
			</mrow>
			</msup>
			<mo>=</mo>
			<mo stretchy="false">(</mo>
			<mroot>
			<mn>2</mn>
			<mn>3</mn>
			</mroot>
			<msup>
			<mo stretchy="false">)</mo>
			<mrow>
			<mi>x</mi>
			</mrow>
			</msup>
			</math>，因为<math display="0">
			<mroot>
			<mn>2</mn>
			<mn>3</mn>
			</mroot>
			<mo>＞</mo>
			<mn>1</mn>
			</math>，所以<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mfrac>
			<mi>x</mi>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			</math>在（-∞，+∞）内是增函数（如图4-7所示）.
			</p>
			<p class="center">
			<img class="img-f" alt="" src="../../assets/images/0137-9.jpg" />
			</p>
			<p class="img">图4-7</p>
			</div>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例3</b></span>　比较下列各题中两个值的大小.
			</span>
			<span class="btn-box" @click="openDialog(thinkThree)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
			<path class="a"
			d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
			transform="translate(-3761 14334.001)" />
			</svg>
			</span>
			</p>
			<p class="p-btn" >
			<span>
			（1） 1.8<sup>2.5</sup>与1.8<sup>3</sup>；
			</span>
			<span class="btn-box" @click="isShowAnswer23 = !isShowAnswer23">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer23" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）因为<i>y</i>=1.8<i><sup>x</sup></i>是<b>R</b>上的增函数，且2.5＜3，所以
			</p>
			<p class="center">1.8<sup>2.5</sup>＜1.8<sup>3</sup>.</p>
			</div>
			<p class="p-btn" >
			<span>
			（2）
			0.9<sup>-0.2</sup>与0.9<sup>-0.3</sup>.
			</span>
			<span class="btn-box" @click="isShowAnswer24 = !isShowAnswer24">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer24" >
			<p>
			<span class="zt-ls"><b>解</b></span>（2）因为<i>y</i>=0.9<i><sup>x</sup></i>是<b>R</b>上的减函数，且-0.2＞-0.3，所以
			</p>
			<p class="center">0.9<sup>-0.2</sup>＜0.9<sup>-0.3</sup>.</p>
			</div>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例4</b></span>　求函数<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msqrt>
			<msup>
			<mn>2</mn>
			<mrow>
			<mi>x</mi>
			</mrow>
			</msup>
			<mo>−</mo>
			<mn>4</mn>
			</msqrt>
			</math>的定义域.
			</span>
			<span class="btn-box" @click="isShowAnswer25 = !isShowAnswer25">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer25" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			要使函数有意义，必须满足2<i><sup>x</sup></i>-4≥0，即2<i><sup>x</sup></i>≥4，又因为<i>y</i>=2<i><sup>x</sup></i>是增函数，所以<i>x</i>≥2.
			</p>
			<p>故函数的定义域为2，+∞）.</p>
			</div>
			<p>
			<span
			class="zt-ls"><b>例5</b></span>　已知指数函数<i>f</i>（<i>x</i>）=<i>a<sup>x</sup></i>（<i>a</i>＞0，且<i>a</i>≠1）的图像过点（3，27）.
			</p>
			<p class="p-btn" >
			<span>
			（1）求<i>f</i>（-1）的值；
			</span>
			<span class="btn-box" @click="isShowAnswer26 = !isShowAnswer26">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer26" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）图像过点（3，27），即<i>x</i>=3时，<i>f</i>（3）=27.
			</p>
			<p>
			由27=<i>a</i><sup>3</sup>，得<i>a</i>=3，即<i>f</i>（<i>x</i>）=3<i><sup>x</sup></i>.
			</p>
			<p>
			所以<math display="0">
			<mi>f</mi>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mn>1</mn>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<msup>
			<mn>3</mn>
			<mrow>
			<mo>−</mo>
			<mn>1</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			</math>.
			</p>
			</div>
			<p class="p-btn" >
			<span>
			（2）
			若<i>f</i>（m）≥9，求<i>m</i>的取值范围.
			</span>
			<span class="btn-box" @click="isShowAnswer27 = !isShowAnswer27">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer27" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			（2）
			因为<i>f</i>（<i>m</i>）=3<i><sup>m</sup></i>，所以得到3<i><sup>m</sup></i>≥9，即3<i><sup>m</sup></i>≥3<sup>2</sup>.
			</p>
			<p>
			函数<i>y</i>=3<i><sup>x</sup></i>在定义域内是增函数.
			</p>
			<p>因此，<i>m</i>≥2，即<i>m</i>的取值范围为[2，+∞）.</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[134]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			</div>
			</div>
			</div>
			<!-- 127 -->
			<div class="page-box" page="134">
			<div v-if="showPageList.indexOf(134) > -1">

			<ul class="page-header-box">
			<li>
			<p>第四单元指数函数与对数函数</p>
			</li>
			<li>
			<p><span>127</span></p>
			</li>
			</ul>

			<div class="padding-116"></div>
			</div>
			<div class="page-box hidePage" page="134">
			</div>

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			@@ -201,15 +3594,18 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<h3 id="c039">习题4.2<span class="fontsz2">＞＞＞</span></h3>
			<div class="bj">
			<examinations :cardList="questionData[135]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			</div>
			</div>
			</div>

			<!-- 129 -->
			<div class="page-box" page="136">
			<div v-if="showPageList.indexOf(136) > -1">

			<ul class="page-header-box">
			<li>
			<p>第四单元指数函数与对数函数</p>
			@@ -218,11 +3614,56 @@
			<p><span>129</span></p>
			</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<h2 id="b024">
			4.3 对数<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			</h2>
			<h3 id="c040">4.3.1 对数的定义<span class="fontsz2">＞＞＞</span></h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/wttc.jpg" />
			</p>
			<p>
			在上一节“观察思考”的情境1中，我们提到了《庄子·天下篇》中的“一尺之棰，日取其半，万世不竭”.现已知“一尺之棰”剩下八分之一尺，请问过去了几天？如果是剩下<i>N</i>尺呢？
			</p>
			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/gn.jpg" />
			</p>
			</div>
			<p class="block">对数</p>
			<p class="block">底数</p>
			<p class="block">真数</p>
			<p class="block">指数式</p>
			<p class="block">对数式</p>
			<p class="block">常用对数</p>
			<p class="block">自然对数</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			一般地，如果<i>a<sup>x</sup></i>=<i>N</i>（<i>a</i>＞0，且<i>a</i>≠1），那么数<i>x</i>叫作以<i>a</i>为底<i>N</i>的<b>对数</b>，记作
			</p>
			<p class="center"><i>x</i>=log<sub>a</sub><i>N</i>.</p>
			<p>
			其中<i>a</i>叫作对数的<b>底数</b>（简称底），<i>N</i>叫作<b>真数</b>.
			</p>
			<p>
			例如，2<sup>3</sup>=8，所以3就是以2为底8的对数，记作3=log
			<sub>2</sub>8；再如，2<i><sup>x</sup></i>=<i>N</i>，所以<i>x</i>是以2为底<i>N</i>的对数，记作<i>x</i>=log
			<sub>2</sub><i>N</i>.
			</p>
			<p>
			式子<i>a<sup>b</sup></i>=<i>N</i>叫作<b>指数式</b>，log
			<i><sub>a</sub>N</i>=<i>b</i>叫作<b>对数式</b>.它们的关系如下.
			</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0140-3.jpg" />
			</p>
			</div>
			</div>
			</div>

			<!-- 130 -->
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			<div v-if="showPageList.indexOf(137) > -1">
			@@ -231,14 +3672,283 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p>
			通常，我们把以10为底的对数叫作<b>常用对数</b>，<i>N</i>的常用对数log
			<sub>10</sub><i>N</i>简记作lg<i>N</i>.例如，log<sub>10</sub>5简记作lg5.
			</p>
			<p>
			另外，在科技、经济以及社会生活中经常使用无理数e，它的值为2.718
			28…，以e为底的对数叫作<b>自然对数</b>.<i>N</i>的自然对数log
			<sub>e</sub><i>N</i>简记作ln<i>N</i>.例如，log<sub>e</sub>8简记作ln8.
			</p>
			<p>根据对数的定义，对数有以下性质.</p>
			<p>（1）零和负数没有对数；</p>
			<p>
			（2） log<i><sub>a</sub></i>1=0，即1的对数为0；
			</p>
			<p>
			（3） log<i><sub>a</sub>a</i>=1，即底数的对数为1.
			</p>
			<div class="bk-hzjl">
			<div class="bj1-hzjl">
			<p class="left">
			<img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
			</p>
			</div>
			<examinations :cardList="questionData[137]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例1</b></span>　把下列指数式写成对数式.
			</span>
			<span class="btn-box" @click="isShowAnswer28 = !isShowAnswer28">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p>
			（1） 5<sup>4</sup>=625；（2）
			<math display="0">
			<msup>
			<mn>8</mn>
			<mrow>
			<mfrac>
			<mn>4</mn>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>=</mo>
			<mn>16</mn>
			</math>；（3） 10<sup>-2</sup>=0.01.
			</p>
			<p v-if="isShowAnswer28" >
			<span class="zt-ls"><b>解</b></span>（1） log<sub>5</sub>625=4；（2）
			<math display="0">
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>8</mn>
			</mrow>
			</msub>
			<mn>16</mn>
			<mo>=</mo>
			<mfrac>
			<mn>4</mn>
			<mn>3</mn>
			</mfrac>
			</math>；（3） lg0.01=-2.
			</p>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例2</b></span>　把下列对数式写成指数式.
			</span>
			<span class="btn-box" @click="isShowAnswer29 = !isShowAnswer29">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p>
			（1） log<sub>3</sub>243=5；（2）
			<math display="0">
			<msub>
			<mi>log</mi>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msub>
			<mfrac>
			<mn>1</mn>
			<mn>27</mn>
			</mfrac>
			<mo>=</mo>
			<mn>3</mn>
			</math>；（3） <i>ln</i>1=0.
			</p>
			<p v-if="isShowAnswer29" >
			<span class="zt-ls"><b>解</b></span>（1） 3<sup>5</sup>=243；（2）
			<math display="0">
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>27</mn>
			</mfrac>
			</math>；（3） <i>e</i><sup>0</sup>=1.
			</p>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例3</b></span>　求下列各式中<i>N</i>的值.
			</span>
			<span class="btn-box" @click="isShowAnswer30 = !isShowAnswer30">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p>
			（1） lg<i>N</i>=-3；（2）
			<math display="0">
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>8</mn>
			</mrow>
			</msub>
			<mi mathvariant="bold">N</mi>
			<mo>=</mo>
			<mfrac>
			<mn>2</mn>
			<mn>3</mn>
			</mfrac>
			</math>.
			</p>
			<div v-if="isShowAnswer30" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）由lg<i>N</i>=-3，得<i>N</i>=10<sup>-3</sup>=0.001；
			</p>
			<p>
			（2）由<math display="0">
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>8</mn>
			</mrow>
			</msub>
			<mi mathvariant="bold">N</mi>
			<mo>=</mo>
			<mfrac>
			<mn>2</mn>
			<mn>3</mn>
			</mfrac>
			</math>，得<math display="0">
			<mi mathvariant="bold">N</mi>
			<mo>=</mo>
			<msup>
			<mn>8</mn>
			<mrow>
			<mfrac>
			<mn>2</mn>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>=</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mfrac>
			<mn>2</mn>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>=</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<mn>4</mn>
			</math>.
			</p>
			</div>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例4</b></span>　求下列各式中<i>x</i>的值.
			</span>
			<span class="btn-box" @click="isShowAnswer31 = !isShowAnswer31">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p>
			（1） log <sub>2</sub>8=<i>x</i>；（2） log
			<sub>4</sub>4<sup>5</sup>=<i>x</i>.
			</p>
			<div v-if="isShowAnswer31" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）由log
			<sub>2</sub>8=<i>x</i>，得2<i><sup>x</sup></i>=8，即2<i><sup>x</sup></i>=2<sup>3</sup>，所以<i>x</i>=3；
			</p>
			<p>
			（2）由log <sub>4</sub>4<sup>5</sup>=<i>x</i>，得4<i><sup>x</sup></i>=4<sup>5</sup>，所以<i>x</i>=5.
			</p>
			</div>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例5</b></span>　求下列各式的值.
			</span>
			<span class="btn-box" @click="isShowAnswer32 = !isShowAnswer32">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			<span class="btn-box" @click="openDialog(thinkFour)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
			<path class="a"
			d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
			transform="translate(-3761 14334.001)" />
			</svg>
			</span>
			</p>
			<p>
			（1） log<sub>5</sub>1；（2） log<sub>7</sub>7；（3） lg 10；（4）
			ln e.
			</p>
			<div v-if="isShowAnswer32" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1） log<sub>5</sub>1=0；（2） log<sub>7</sub>7=1；
			</p>
			<p>（3） lg10=log<sub>10</sub>10=1；（4） ln e=log<sub>e</sub>e=1.</p>
			</div>
			</div>
			</div>
			</div>

			<!-- 131 -->
			<div class="page-box" page="138">
			<div v-if="showPageList.indexOf(138) > -1">

			<ul class="page-header-box">
			<li>
			<p>第四单元指数函数与对数函数</p>
			@@ -247,26 +3957,792 @@
			<p><span>131</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[138]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			<h3 id="c041">
			4.3.2 对数的运算性质<span class="fontsz2">＞＞＞</span>
			</h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/gcsk.jpg" />
			</p>
			<p>
			利用对数式与指数式的关系，填写表4-4，猜想对数的运算性质，并与同学交流.
			</p>
			<p class="img">表4-4</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0142-8.jpg" />
			</p>
			</div>
			</div>
			</div>

			<!-- 132 -->
			<div class="page-box" page="139">
			<div v-if="showPageList.indexOf(139) > -1">

			<ul class="page-header-odd fl al-end">
			<li>132</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>我们可以得到两个正数的积、商、幂的对数运算性质.</p>
			<p>
			（1）
			积的对数：<b>两个正数积的对数，等于同一底数的这两个数的对数的和</b>，即
			</p>
			<p class="center">
			log<i><sub>a</sub></i>（<i>MN</i>）=log<i><sub>a</sub>M</i>+log
			<i><sub>a</sub>N</i>（<i>a</i>＞0，且<i>a</i>≠1）.
			</p>
			<p>
			<b>证明</b> 设log<i><sub>a</sub>M</i>=<i>p</i>，log<i><sub>a</sub>N</i>=<i>q</i>，
			</p>
			<p>
			根据对数的定义，得<i>M</i>=<i>a<sup>p</sup></i>，<i>N</i>=<i>a<sup>q</sup></i>，
			</p>
			<p>
			所以 <i>MN</i>=<i>a<sup>p</sup> a<sup>q</sup></i>=<i>a<sup>p+q</sup></i>.
			</p>
			<p>把指数式化为对数式，得</p>
			<p class="center">
			log<i><sub>a</sub></i>（<i>MN</i>）=<i>p</i>+<i>q</i>=log<i><sub>a</sub>M</i>+log<i><sub>a</sub>N</i>.
			</p>
			<p>
			（2）
			商的对数：<b>两个正数商的对数，等于同一底数的被除数的对数减去除数的对数，</b>即
			</p>
			<math display="block">
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>M</mi>
			<mi mathvariant="bold">N</mi>
			</mfrac>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>M</mi>
			<mo>−</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi mathvariant="bold">N</mi>
			<mo stretchy="false">(</mo>
			<mi>a</mi>
			<mo>></mo>
			<mn>0</mn>
			<mtext>, 且 </mtext>
			<mi>a</mi>
			<mo>≠</mo>
			<mn>1</mn>
			<mo stretchy="false">)</mo>
			<mtext>. </mtext>
			</math>
			<p>
			（3）
			幂的对数：<b>一个正数幂的对数，等于幂指数乘这个数的对数，</b>即
			</p>
			<p class="center">
			log<i><sub>a</sub>M<sup>q</sup></i>=<i>q</i>log
			<i><sub>a</sub>M</i>（<i>a</i>＞0，且<i>a</i>≠1，<i>q</i>∈<b>R</b>）.
			</p>
			<p>
			特别地，log<i><sub>a</sub>a<sup>b</sup></i>=<i>b</i>（<i>a</i>＞0，且<i>a</i>≠1）.
			</p>
			<div class="bk-hzjl">
			<div class="bj1-hzjl">
			<p class="left">
			<img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
			</p>
			</div>
			<examinations :cardList="questionData[139]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			<p class="p-btn" >
			<span>
			<span
			class="zt-ls"><b>例1</b></span>　用log<i><sub>a</sub>x</i>，log<i><sub>a</sub>y</i>，log<i><sub>a</sub>z</i>表示下列各式（式中字母均为正实数且<i>a</i>≠1）.
			</span>
			<span class="btn-box" @click="openDialog(thinkFive)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
			<path class="a"
			d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
			transform="translate(-3761 14334.001)" />
			</svg>
			</span>
			</p>
			<p class="p-btn" >
			<span>
			（1） log<i><sub>a</sub></i>（<i>x</i><sup>2</sup><i>yz</i><sup>3</sup>）；
			</span>
			<span class="btn-box" @click="isShowAnswer33 = !isShowAnswer33">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer33" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			</p>
			<p class="left1">
			<math display="">
			<mo stretchy="false">（1）</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mi>x</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mi>y</mi>
			<msup>
			<mi>z</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mi>x</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo>+</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>y</mi>
			<mo>+</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mi>z</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<mn>2</mn>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>+</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>y</mi>
			<mo>+</mo>
			<mn>3</mn>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>z</mi>
			<mo>;</mo>
			</math>
			</p>
			</div>
			<p class="p-btn" >
			<span>
			（2）<math display="0">
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<msup>
			<mi>x</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mrow>
			<mi>y</mi>
			<mi>z</mi>
			</mrow>
			</mfrac>
			</math>；
			</span>
			<span class="btn-box" @click="isShowAnswer34 = !isShowAnswer34">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p class="left1" v-if="isShowAnswer34">
			<math display="">
			<mo stretchy="false">（2）</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<msup>
			<mi>x</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mrow>
			<mi>y</mi>
			<mi>z</mi>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mi>x</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo>−</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mo stretchy="false">(</mo>
			<mi>y</mi>
			<mi>z</mi>
			<mo stretchy="false">)</mo>
			<mo>=</mo>
			<mn>2</mn>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>−</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>y</mi>
			<mo>+</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>z</mi>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mn>2</mn>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>−</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>y</mi>
			<mo>−</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>z</mi>
			<mo>;</mo>
			</math>
			</p>
			<p class="p-btn" >
			<span>
			（3）
			<math display="0">
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<msqrt>
			<mi>x</mi>
			</msqrt>
			<mrow>
			<msup>
			<mi>y</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mi>z</mi>
			</mrow>
			</mfrac>
			</math>.
			</span>
			<span class="btn-box" @click="isShowAnswer35 = !isShowAnswer35">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p class="left1" v-if="isShowAnswer35" >
			<math display="">
			<mo stretchy="false">（3）</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<msqrt>
			<mi>x</mi>
			</msqrt>
			<mrow>
			<msup>
			<mi>y</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mi>z</mi>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msqrt>
			<mi>x</mi>
			</msqrt>
			<mo>−</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mi>y</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mi>z</mi>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>−</mo>
			<mn>2</mn>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>y</mi>
			<mo>−</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>z</mi>
			<mo>.</mo>
			</math>
			</p>
			<p>
			<span class="zt-ls"><b>例2</b></span>　计算.
			</p>
			<p class="p-btn" >
			<span>
			（1）
			<math display="0">
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>5</mn>
			</mrow>
			</msub>
			<mroot>
			<mn>25</mn>
			<mn>3</mn>
			</mroot>
			</math>；
			</span>
			<span class="btn-box" @click="isShowAnswer36 = !isShowAnswer36">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer36" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			</p>
			<p class="left1">
			<math display="">
			<mo stretchy="false">（1）</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>5</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mroot>
			<mn>25</mn>
			<mn>3</mn>
			</mroot>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>5</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mroot>
			<msup>
			<mn>5</mn>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mn>3</mn>
			</mroot>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>5</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>5</mn>
			<mrow>
			<mfrac>
			<mn>2</mn>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			<mo>=</mo>
			<mfrac>
			<mn>2</mn>
			<mn>3</mn>
			</mfrac>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>5</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>5</mn>
			<mo>=</mo>
			<mfrac>
			<mn>2</mn>
			<mn>3</mn>
			</mfrac>
			<mo>;</mo>
			</math>
			</p>
			</div>
			<p class="p-btn" >
			<span>
			（2） log <sub>3</sub>（9<sup>3</sup>×3<sup>5</sup>）；
			</span>
			<span class="btn-box" @click="isShowAnswer37 = !isShowAnswer37">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer37" class="left1">
			<math display="">
			<mo stretchy="false">（2）</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mn>9</mn>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mo>×</mo>
			<msup>
			<mn>3</mn>
			<mrow>
			<mn>5</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>9</mn>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mo>+</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>3</mn>
			<mrow>
			<mn>5</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>3</mn>
			<mrow>
			<mn>6</mn>
			</mrow>
			</msup>
			<mo>+</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>3</mn>
			<mrow>
			<mn>5</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<mn>6</mn>
			<mo>+</mo>
			<mn>5</mn>
			<mo>=</mo>
			<mn>11</mn>
			<mo>;</mo>
			</math>
			</p>
			<p class="p-btn" >
			<span>
			（3） log
			<sub>7</sub>56-log<sub>7</sub>8.
			</span>
			<span class="btn-box" @click="isShowAnswer38 = !isShowAnswer38">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer38" class="left1">
			<math display="">
			<mo stretchy="false">（3）</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>7</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>56</mn>
			<mo>−</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>7</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>8</mn>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>7</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mn>56</mn>
			<mn>8</mn>
			</mfrac>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>7</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>7</mn>
			<mo>=</mo>
			<mn>1</mn>
			<mo>.</mo>
			</math>
			</p>
			</div>
			</div>
			</div>
			<!-- 133 -->
			<div class="page-box" page="140">
			<div v-if="showPageList.indexOf(140) > -1">

			<ul class="page-header-box">
			<li>
			<p>第四单元指数函数与对数函数</p>
			@@ -276,10 +4752,217 @@
			</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">



			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[140]" :hideCollect="true" sourceType="json" inputBc="#d3edfa" v-if="questionData">
			</examinations>
			</div>
			<h3 id="c042">
			4.3.3（选学）换底公式、对数恒等式<span class="fontsz2">＞＞＞</span>
			</h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			设log<i><sub>a</sub>N</i>=<i>x</i>，则<i>a<sup>x</sup></i>=<i>N</i>，两边取以<i>c</i>为底的对数，得log<i><sub>c</sub>a<sup>x</sup></i>=log<i><sub>c</sub>N</i>，于是<i>x</i>log<i><sub>c</sub>a</i>=log<i><sub>c</sub>N</i>，即<math
			display="0">
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>c</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi mathvariant="bold">N</mi>
			</mrow>
			<mrow>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>c</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>a</mi>
			</mrow>
			</mfrac>
			</math>，所以<math display="0">
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi mathvariant="bold">N</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>c</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi mathvariant="bold">N</mi>
			</mrow>
			<mrow>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>c</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>a</mi>
			</mrow>
			</mfrac>
			</math>.
			</p>
			<p>于是，我们有<b>对数的换底公式：</b></p>
			<math display="block">
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>b</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>c</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>b</mi>
			</mrow>
			<mrow>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>c</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>a</mi>
			</mrow>
			</mfrac>
			<mo stretchy="false">(</mo>
			<mi>a</mi>
			<mo>></mo>
			<mn>0</mn>
			<mo>,</mo>
			<mtext> 且 </mtext>
			<mi>a</mi>
			<mo>≠</mo>
			<mn>1</mn>
			<mo>;</mo>
			<mi>c</mi>
			<mo>></mo>
			<mn>0</mn>
			<mtext>, 且 </mtext>
			<mi>c</mi>
			<mo>≠</mo>
			<mn>1</mn>
			<mo stretchy="false">)</mo>
			<mtext>. </mtext>
			</math>
			<p>特别地，</p>
			<math display="block">
			<mtable columnalign="left" columnspacing="1em" rowspacing="4pt">
			<mtr>
			<mtd>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>b</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>b</mi>
			</mrow>
			<mrow>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>a</mi>
			</mrow>
			</mfrac>
			<mo stretchy="false">(</mo>
			<mi>a</mi>
			<mo>></mo>
			<mn>0</mn>
			<mo>,</mo>
			<mtext> 且 </mtext>
			<mi>a</mi>
			<mo>≠</mo>
			<mn>1</mn>
			<mo stretchy="false">)</mo>
			<mo>;</mo>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>b</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>ln</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>b</mi>
			</mrow>
			<mrow>
			<mi>ln</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>a</mi>
			</mrow>
			</mfrac>
			<mo stretchy="false">(</mo>
			<mi>a</mi>
			<mo>></mo>
			<mn>0</mn>
			<mo>,</mo>
			<mtext> 且 </mtext>
			<mi>a</mi>
			<mo>≠</mo>
			<mn>1</mn>
			<mo stretchy="false">)</mo>
			<mo>.</mo>
			</mtd>
			</mtr>
			</mtable>
			</math>
			</div>
			</div>
			</div>

			<!-- 134 -->
			<div class="page-box" page="141">
			<div v-if="showPageList.indexOf(141) > -1">
			@@ -288,14 +4971,557 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例1</b></span>　求log<sub>27</sub>8·log <sub>32</sub>9的值.
			</span>
			<span class="btn-box" @click="isShowAnswer39 = !isShowAnswer39">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer39" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			</p>
			<math display="block">
			<mtable displaystyle="true" columnalign="right left right left right left right left right left right left"
			columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" rowspacing="3pt">
			<mtr>
			<mtd>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>27</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>8</mn>
			<mo>⋅</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>32</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>9</mn>
			</mtd>
			<mtd>
			<mi></mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>8</mn>
			</mrow>
			<mrow>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>27</mn>
			</mrow>
			</mfrac>
			<mo>⋅</mo>
			<mfrac>
			<mrow>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>9</mn>
			</mrow>
			<mrow>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>32</mn>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			</mrow>
			<mrow>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>3</mn>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			</mrow>
			</mfrac>
			<mo>⋅</mo>
			<mfrac>
			<mrow>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>3</mn>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			</mrow>
			<mrow>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>5</mn>
			</mrow>
			</msup>
			</mrow>
			</mfrac>
			</mtd>
			</mtr>
			<mtr>
			<mtd></mtd>
			<mtd>
			<mi></mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>2</mn>
			</mrow>
			<mrow>
			<mn>3</mn>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>3</mn>
			</mrow>
			</mfrac>
			<mo>⋅</mo>
			<mfrac>
			<mrow>
			<mn>2</mn>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>3</mn>
			</mrow>
			<mrow>
			<mn>5</mn>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>2</mn>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mn>2</mn>
			<mn>5</mn>
			</mfrac>
			<mo>.</mo>
			</mtd>
			</mtr>
			</mtable>
			</math>
			</div>
			<p class="p-btn" >
			<span>
			<span
			class="zt-ls"><b>例2</b></span>　求证：log<i><sub>a</sub>b</i>·log<i><sub>b</sub>c</i>·log<i><sub>c</sub>a</i>=1（<i>a</i>，<i>b</i>，<i>c</i>均为正实数，且均不等于1）.
			</span>
			<span class="btn-box" @click="isShowAnswer40 = !isShowAnswer40">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer40" >
			<p>
			<b>证明</b>
			<math display="0">
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>b</mi>
			<mo>⋅</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>b</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>c</mi>
			<mo>⋅</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>c</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>a</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>b</mi>
			</mrow>
			<mrow>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>a</mi>
			</mrow>
			</mfrac>
			<mo>⋅</mo>
			<mfrac>
			<mrow>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>c</mi>
			</mrow>
			<mrow>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>b</mi>
			</mrow>
			</mfrac>
			<mo>⋅</mo>
			<mfrac>
			<mrow>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>a</mi>
			</mrow>
			<mrow>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>c</mi>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mn>1</mn>
			</math>.
			</p>
			<p>设</p>
			<math display="block">
			<msup>
			<mi>a</mi>
			<mrow>
			<mi>b</mi>
			</mrow>
			</msup>
			<mo>=</mo>
			<mi mathvariant="bold">N</mi>
			<mo stretchy="false">(</mo>
			<mi>a</mi>
			<mo>></mo>
			<mn>0</mn>
			<mtext>, 且 </mtext>
			<mi>a</mi>
			<mo>≠</mo>
			<mn>1</mn>
			<mo stretchy="false">)</mo>
			<mtext>, </mtext>
			</math>
			<p class="right">①</p>
			<p>由对数定义得</p>
			<math display="block">
			<mi>b</mi>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mi mathvariant="bold">N</mi>
			<mo>，</mo>
			</math>
			<p class="right">②</p>
			<p>把②代入①中，得</p>
			<math display="block">
			<msup>
			<mi>a</mi>
			<mrow>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi mathvariant="bold">N</mi>
			</mrow>
			</msup>
			<mo>=</mo>
			<mi mathvariant="bold">N</mi>
			<mo stretchy="false">(</mo>
			<mi>a</mi>
			<mo>></mo>
			<mn>0</mn>
			<mtext>, 且 </mtext>
			<mi>a</mi>
			<mo>≠</mo>
			<mn>1</mn>
			<mo stretchy="false">)</mo>
			<mtext>. </mtext>
			</math>
			<p>这个式子叫<b>对数恒等式</b>.</p>
			</div>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例3</b></span>　求下列各式的值.
			</span>
			<span class="btn-box" @click="isShowAnswer41 = !isShowAnswer41">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p>
			（1）
			<math display="0">
			<msup>
			<mn>2</mn>
			<mrow>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msub>
			<mn>7</mn>
			</mrow>
			</msup>
			</math>；（2）
			<math display="0">
			<msup>
			<mn>4</mn>
			<mrow>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msub>
			<mn>7</mn>
			</mrow>
			</msup>
			</math>；（3）
			<math display="0">
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>1</mn>
			<mo>+</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msub>
			<mn>7</mn>
			</mrow>
			</msup>
			</math>.
			</p>
			<div v-if="isShowAnswer41" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			</p>
			<p class="left1">
			<math display="">
			<mo stretchy="false">（1）</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>7</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<mn>7</mn>
			<mo>;</mo>
			</math>
			</p>
			<p class="left1">
			<math display="">
			<mo stretchy="false">（2）</mo>
			<msup>
			<mn>4</mn>
			<mrow>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>7</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>7</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>2</mn>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>7</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>7</mn>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			</mrow>
			</msup>
			<mo>=</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>49</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<mn>49</mn>
			<mo>;</mo>
			</math>
			</p>
			<p class="left1">
			<math display="">
			<mo stretchy="false">（3）</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>1</mn>
			<mo>+</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>7</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<mn>1</mn>
			</mrow>
			</msup>
			<mo>×</mo>
			<msup>
			<mn>2</mn>
			<mrow>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>7</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<mn>2</mn>
			<mo>×</mo>
			<mn>7</mn>
			<mo>=</mo>
			<mn>14</mn>
			<mo>.</mo>
			</math>
			</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[141]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			</div>
			</div>
			</div>

			<!-- 135 -->
			<div class="page-box" page="142">
			<div v-if="showPageList.indexOf(142) > -1">

			<ul class="page-header-box">
			<li>
			<p>第四单元指数函数与对数函数</p>
			@@ -304,10 +5530,28 @@
			<p><span>135</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<h3 id="c043">习题4.3<span class="fontsz2">＞＞＞</span></h3>
			<div class="bj">
			<examinations :cardList="questionData[142]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			<h2 id="b025">
			4.4 对数函数<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			</h2>
			<h3 id="c044">
			4.4.1 对数函数的定义<span class="fontsz2">＞＞＞</span>
			</h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/wttc.jpg" />
			</p>
			<p>
			在第二节“观察思考”的情境2中，细胞由1个分裂为2个，2个分裂为4个……如果已知分裂<i>x</i>次后对应细胞数量是1
			024个，那么如何求分裂的次数<i>x</i>呢？
			</p>
			</div>
			</div>
			</div>

			<!-- 136 -->
			<div class="page-box" page="143">
			<div v-if="showPageList.indexOf(143) > -1">
			@@ -317,14 +5561,199 @@
			<li>上册</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			设1个细胞经过<i>y</i>次分裂后得到<i>x</i>个细胞，则<i>x</i>与<i>y</i>的函数关系式为<i>x</i>=2<i><sup>y</sup></i>，将此指数式写为对数式，得到
			</p>
			<p class="center"><i>y</i>=log<sub>2</sub><i>x</i>.</p>
			<p>这个式子就是用分裂后的细胞数量<i>x</i>来表示分裂的次数<i>y</i>.</p>
			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/gn.jpg" />
			</p>
			</div>
			<p class="block">对数函数</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			通过指数与对数的关系我们观察到：<i>y</i>=log<sub>2</sub><i>x</i>是一个函数，其自变量<i>x</i>位于真数位置，底数是常数.类比指数函数定义的学习过程，我们可以用字母<i>a</i>代替底数2，即有<i>y</i>=log<sub>a</sub><i>x</i>（<i>a</i>＞0，且<i>a</i>≠1）这类特征的函数.
			</p>
			<p>
			一般地，形如<i>y</i>=log<i><sub>a</sub>x</i>（<i>a</i>＞0，且<i>a</i>≠1）的函数叫作<b>对数函数</b>，其中<i>x</i>是自变量，函数的定义域为（0，+∞）.
			</p>
			<p>
			例如，<i>y</i>=log<sub>2</sub><i>x</i>，<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			</math>，<i>y</i>=lg <i>x</i>，<i>y</i>=ln <i>x</i>都是对数函数.
			</p>
			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" />
			</p>
			</div>
			<p class="block">
			1.对数函数与指数函数的底数<i>a</i>的取值范围保持一致.
			</p>
			<p class="block">2.由于对数的</p>
			<p class="block">
			真数的取值范围为（0，+∞），所以对数函数自变量<i>x</i>的取值范围为（0，+∞）.
			</p>
			</div>
			<p class="p-btn" >
			<span>
			<span
			class="zt-ls"><b>例1</b></span>　已知对数函数<i>f</i>（<i>x</i>）=log<i><sub>a</sub>x</i>（<i>a</i>＞0，且<i>a</i>≠1），且<i>f</i>（9）=
			2，求<i>f</i>（3），<i>f</i>（1），<math display="0">
			<mi>f</mi>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>1</mn>
			<mn>27</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>的值.
			</span>
			<span class="btn-box" @click="isShowAnswer42 = !isShowAnswer42">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			<span class="btn-box" @click="openDialog(thinkSix)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
			<path class="a"
			d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
			transform="translate(-3761 14334.001)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer42" >
			<p>
			<span class="zt-ls"><b>解</b></span> 因为<i>f</i>（9）=2，得2=log<i><sub>a</sub></i>9.
			</p>
			<p>于是<i>a</i><sup>2</sup>=9，得<i>a</i>=3，</p>
			<p>函数解析式为<i>f</i>（<i>x</i>）=log<sub>3</sub><i>x</i>.</p>
			<p>
			所以<i>f</i>（3）=log<sub>3</sub>3=1，
			<i>f</i>（1）=log<sub>3</sub>1=0，
			</p>
			<p>
			<math display="0">
			<mi>f</mi>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>1</mn>
			<mn>27</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mn>1</mn>
			<mn>27</mn>
			</mfrac>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>3</mn>
			<mrow>
			<mo>−</mo>
			<mn>3</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<mo>−</mo>
			<mn>3</mn>
			</math>.
			</p>
			</div>
			<p>
			<span class="zt-ls"><b>例2</b></span>　求下列函数的定义域.
			</p>
			<p class="p-btn" >
			<span>
			（1） <i>y</i>=log <sub>0.5</sub>（<i>x</i>-3）；
			</span>
			<span class="btn-box" @click="isShowAnswer43 = !isShowAnswer43">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer43" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）要使函数有意义，必须满足<i>x</i>-3＞0，解得<i>x</i>＞3.
			</p>
			<p>
			所以，<i>y</i>=log <sub>0.5</sub>（<i>x</i>-3）的定义域是（3，+∞）.
			</p>
			</div>
			<p class="p-btn" >
			<span>
			（2）
			<i>y</i>=log<sub>3</sub>（4-<i>x</i><sup>2</sup>）.
			</span>
			<span class="btn-box" @click="isShowAnswer44 = !isShowAnswer44">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer44" >
			<p>
			<span class="zt-ls"><b>解</b></span>（2）要使函数有意义，必须满足4-<i>x</i><sup>2</sup>＞0，解得
			-2＜<i>x</i>＜2.
			</p>
			<p>
			所以，<i>y</i>=log<sub>3</sub>（4-<i>x</i><sup>2</sup>）的定义域是（-2，2）.
			</p>
			</div>
			</div>
			</div>
			</div>

			<!-- 137 -->
			<div class="page-box" page="144">
			<div v-if="showPageList.indexOf(144) > -1">

			<ul class="page-header-box">
			<li>
			<p>第四单元指数函数与对数函数</p>
			@@ -334,27 +5763,165 @@
			</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[144]" :hideCollect="true" sourceType="json" inputBc="#d3edfa" v-if="questionData">
			</examinations>
			</div>
			<h3 id="c045">
			4.4.2 对数函数的图像与性质<span class="fontsz2">＞＞＞</span>
			</h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/gcsk.jpg" />
			</p>
			<p>
			与研究指数函数的图像和性质一样，我们首先通过描点法画出对数函数的图像，然后归纳总结函数的相关性质.下面我们以<i>y</i>=log<sub>2</sub><i>x</i>和<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			</math>为例画出对数函数的图像，通过观察其图像特征，归纳出对数函数的性质.
			</p>
			<p>第一步：计算部分数值并列表（如表4-5所示）.</p>
			<p class="img">表4-5</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0148-3.jpg" />
			</p>
			<p>
			第二步：描点，并用光滑的曲线连接所描的点，画出它们的图像，如图4-8所示.
			</p>
			<p>
			利用相同方法，我们还可以在同一平面直角坐标系中画出<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mfrac>
			<mn>3</mn>
			<mn>2</mn>
			</mfrac>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			</math>，<i>y</i>=log <sub>2</sub><i>x</i>，<i>y</i>=log <sub>0.08</sub><i>x</i>，<i>y</i>=log
			<sub>4.5</sub><i>x</i>，<i>y</i>=log
			<sub>0.6</sub><i>x</i>，<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			</math>的图像，如图4-9所示.
			</p>
			</div>
			</div>
			</div>

			<!-- 138 -->
			<div class="page-box" page="145">
			<div v-if="showPageList.indexOf(145) > -1">

			<ul class="page-header-odd fl al-end">
			<li>138</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="center">
			<img class="img-b" alt="" src="../../assets/images/0149-1.jpg" />
			</p>
			<p class="img">图4-8</p>
			<p class="center">
			<img class="img-d" alt="" src="../../assets/images/0149-2.jpg" />
			</p>
			<p class="img">图4-9</p>
			<p><b>类比归纳</b></p>
			<p>
			类比指数函数图像特征的观察方法，观察对数函数的图像，描述它们的图像在位置、公共点和变化趋势等方面的共性特征.
			</p>
			<p>
			（1）
			图中所有对数函数的图像均在<i>y</i>轴的右侧（<b>位置特征</b>）；
			</p>
			<p>
			（2）
			图中所有对数函数的图像都经过定点（1，0）（<b>公共点特征</b>）；
			</p>
			<p>
			（3）在定义域内，对数函数<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mfrac>
			<mn>3</mn>
			<mn>2</mn>
			</mfrac>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			</math>，<i>y</i>=log <sub>2</sub><i>x</i>，<i>y</i>=log
			<sub>4.5</sub><i>x</i>图像从左到右分别逐渐上升，在第四象限内向下与<i>y</i>轴无限接近；对数函数<i>y</i>=log
			<sub>0.08</sub><i>x</i>，<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			</math>，<i>y</i>=log <sub>0.6</sub><i>x</i>图像从左到右分别逐渐下降，在第一象限内向上与<i>y</i>轴无限接近（<b>变化趋势特征</b>）.
			</p>
			<p>
			类比指数函数的图像，对数函数<i>y</i>=log<i><sub>a</sub>x</i>（<i>a</i>＞0，且<i>a</i>≠1）的图像按底数<i>a</i>的取值，可分为0＜<i>a</i>＜1和<i>a</i>＞1两种类型，我们从指数式与对数式的关系也可发现.
			</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			一般地，对数函数<i>y</i>=log<i><sub>a</sub>x</i>（<i>a</i>＞0，且<i>a</i>≠1）具有下列性质.
			</p>
			<p>（1）函数的定义域为（0，+∞），值域为<b>R</b>；</p>
			<p>（2）当<i>x</i>=1时，函数值<i>y</i>=0；</p>
			<p>
			（3）
			当<i>a</i>＞1时，函数在（0，+∞）内是增函数；当0＜<i>a</i>＜1时，函数在（0，+∞）内是减函数.
			</p>
			<p>对数函数的图像和性质可以总结如表4-6所示.</p>
			</div>
			</div>
			</div>

			<!-- 139 -->
			<div class="page-box" page="146">
			<div v-if="showPageList.indexOf(146) > -1">

			<ul class="page-header-box">
			<li>
			<p>第四单元指数函数与对数函数</p>
			@@ -363,10 +5930,114 @@
			<p><span>139</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="img">表4-6</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0150-1.jpg" />
			</p>
			<div class="bk-hzjl">
			<div class="bj1-hzjl">
			<p class="left">
			<img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
			</p>
			</div>
			<examinations :cardList="questionData[146]" :hideCollect="true" sourceType="json"
			v-if="questionData" ></examinations>
			</div>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例1</b></span>　比较下列各组数中两个值的大小.
			</span>
			<span class="btn-box" @click="openDialog(thinkSeven)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
			<path class="a"
			d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
			transform="translate(-3761 14334.001)" />
			</svg>
			</span>
			</p>
			<p class="p-btn" >
			<span>
			（1） log<sub>2</sub>5.3 与log<sub>2</sub>4.7；
			</span>
			<span class="btn-box" @click="isShowAnswer45 = !isShowAnswer45">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer45" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）
			因为底数2＞1，所以<i>y</i>=log<sub>2</sub><i>x</i>在区间（0，+∞）上是增函数，函数图像如图4-10所示.
			</p>
			<p>又因为5.3＞4.7，所以log<sub>2</sub>5.3＞log<sub>2</sub>4.7.</p>
			<p class="center">
			<img class="img-f" alt="" src="../../assets/images/0151-1.jpg" />
			</p>
			<p class="img">图4-10</p>
			</div>
			<p class="p-btn" >
			<span>
			（2） log
			<sub>0.2</sub>7与log <sub>0.2</sub>9；
			</span>
			<span class="btn-box" @click="isShowAnswer46 = !isShowAnswer46">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer46" >
			<p>
			<span class="zt-ls"><b>解</b></span>（2）因为底数0＜0.2＜1，所以<i>y</i>=log <sub>0.2</sub><i>x</i>在区间（0，+∞）上是减函数，函数图像如图4-11所示.
			</p>
			<p>又因为7＜9，所以log <sub>0.2</sub>7＞log <sub>0.2</sub>9.</p>
			<p class="center">
			<img class="img-f" alt="" src="../../assets/images/0151-2.jpg" />
			</p>
			<p class="img">图4-11</p>
			</div>
			<p class="p-btn" >
			<span>
			（3） log<sub>5</sub>4与1；
			</span>
			<span class="btn-box" @click="isShowAnswer47 = !isShowAnswer47">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer47">
			<span class="zt-ls"><b>解</b></span> （3） log<sub>5</sub>4＜log<sub>5</sub>5=1，即log<sub>5</sub>4＜1.
			</p>
			<p class="p-btn" >
			<span>
			（4）log<sub>3</sub>4与log
			<sub>0.3</sub>4.
			</span>
			<span class="btn-box" @click="isShowAnswer48 = !isShowAnswer48">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer48" >
			<span class="zt-ls"><b>解</b></span>（4）因为 log<sub>3</sub>4＞log<sub>3</sub>1=0，log
			<sub>0.3</sub>4＜log <sub>0.3</sub>1=0，所以 log<sub>3</sub>4＞log
			<sub>0.3</sub>4.
			</p>
			</div>
			</div>
			</div>

			<!-- 140 -->
			<div class="page-box" page="147">
			<div v-if="showPageList.indexOf(147) > -1">
			@@ -375,98 +6046,402 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p>
			<span class="zt-ls"><b>例2</b></span>　解下列不等式.
			</p>
			<p class="p-btn" >
			<span>
			（1）log <sub>4</sub><i>x</i>＜log<sub>4</sub>5；
			</span>
			<span class="btn-box" @click="isShowAnswer49 = !isShowAnswer49">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer49" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）因为<i>y</i>=log
			4<i>x</i>在（0，+∞）上是增函数，所以<i>x</i>＜5.
			</p>
			<p>又因为<i>x</i>＞0，所以0＜<i>x</i>＜5.</p>
			<p>所以不等式的解集为（0，5）.</p>
			</div>
			<p class="p-btn" >
			<span>
			（2）
			<math display="0">
			<msub>
			<mi>log</mi>
			<mrow>
			<mfrac>
			<mn>4</mn>
			<mn>5</mn>
			</mfrac>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>＞</mo>
			<mn>1</mn>
			</math>.
			</span>
			<span class="btn-box" @click="isShowAnswer50 = !isShowAnswer50">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer50" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			（2）
			<math display="0">
			<msub>
			<mi>log</mi>
			<mrow>
			<mfrac>
			<mn>4</mn>
			<mn>5</mn>
			</mfrac>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>＞</mo>
			<mn>1</mn>
			</math>，即<math display="0">
			<msub>
			<mi>log</mi>
			<mrow>
			<mfrac>
			<mn>4</mn>
			<mn>5</mn>
			</mfrac>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>></mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mfrac>
			<mn>4</mn>
			<mn>5</mn>
			</mfrac>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mn>4</mn>
			<mn>5</mn>
			</mfrac>
			</math>.
			</p>
			<p>
			因为<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mfrac>
			<mn>4</mn>
			<mn>5</mn>
			</mfrac>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			</math>在（0，+∞）上是减函数，所以<math display="0">
			<mi>x</mi>
			<mo>＜</mo>
			<mfrac>
			<mn>4</mn>
			<mn>5</mn>
			</mfrac>
			</math>.
			</p>
			<p>
			又因为<i>x</i>＞0，所以<math display="0">
			<mn>0</mn>
			<mo>＜</mo>
			<mi>x</mi>
			<mo>＜</mo>
			<mfrac>
			<mn>4</mn>
			<mn>5</mn>
			</mfrac>
			</math>.
			</p>
			<p>
			所以不等式的解集为（0，<math display="0">
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mn>0</mn>
			<mo>，</mo>
			<mfrac>
			<mn>4</mn>
			<mn>5</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>）.
			</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[147]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			</div>
			</div>
			</div>

			<!-- 141 -->
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			<ul class="page-header-box">
			<li>
			<p>第四单元指数函数与对数函数</p>
			</li>
			<li>
			<p><span>141</span></p>
			<p><span>141-142</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<h3 id="c046">习题4.4<span class="fontsz2">＞＞＞</span></h3>
			<div class="bj">
			<examinations :cardList="questionData[148]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			<h2 id="b026">
			4.5 指数函数与对数函数的实际应用<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			</h2>
			<p>
			我们学习的基本初等函数，可以描述、刻画客观世界中某一类事物运动变化的规律.例如，用一次函数模型可以描述生活中的“线性增长”（直线增长）现象.利用指数函数与对数函数的相关知识建立函数模型，可以描述、刻画科学与技术、经济与社会、生产与生活中的“指数增长”和“对数增长”现象.
			</p>
			<p>
			<span
			class="zt-ls"><b>例1</b></span>　开展人口普查，对于调整、完善人口政策，推动人口结构优化，促进人口素质提升具有重要意义.第七次全国人口普查结果显示，2020年年末全国大陆总人口为141
			178万人，其中城镇常住人口90
			199万人，占总人口的比例（常住人口城镇化率）为63.89%，与2010年相比，提高了14.21个百分点.
			</p>
			<p class="p-btn" >
			<span>
			（1）假设此后每年都增加700万人口，20年后我国大陆人口总数是多少？
			</span>
			<span class="btn-box" @click="isShowAnswer51 = !isShowAnswer51">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			<span class="btn-box" @click="openDialog(thinkEight)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
			<path class="a"
			d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
			transform="translate(-3761 14334.001)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer51" >
			<span class="zt-ls"><b>解</b></span>（1）因为每年增加700万人口，20年共增加20×700万=14
			000万人口，因此20年后我国大陆人口为155 178万（15.517 8亿）.
			</p>
			</div>
			</div>
			</div>

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			<div v-if="showPageList.indexOf(149) > -1">
			<ul class="page-header-odd fl al-end">
			<li>142</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			</div>
			<div class="page-box hidePage" page="149">
			</div>

			<!-- 143 -->
			<div class="page-box" page="150">
			<div v-if="showPageList.indexOf(150) > -1">


			<ul class="page-header-box">
			<li>
			<p>第四单元指数函数与对数函数</p>
			</li>
			<li>
			<p><span>143</span></p>
			<p><span>143-144</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="p-btn" >
			<span>
			（2）
			假设此后每年人口的平均增长率是1%（每年都在前一年基础上增加1%），20年后我国大陆人口总数约为多少？（单位：万，结果精确到0.01）
			</span>
			<span class="btn-box" @click="isShowAnswer52 = !isShowAnswer52">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			<span class="btn-box" @click="openDialog(thinkNine)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
			<path class="a"
			d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
			transform="translate(-3761 14334.001)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer52" >
			<p>（2）设经过<i>x</i>年，我国人口为<i>y</i>万，由题意得</p>
			<p class="center">
			<i>y</i>=141 178（1+1%）<i><sup>x</sup></i>.
			</p>
			<p>当<i>x</i>=20时，<i>y</i>=141 178（1+1%）<sup>20</sup>.</p>
			<p>利用科学计算器可求得<i>y</i>≈172 263.99万.</p>
			<p>
			所以，假设每年都增加700万人口，20年后我国大陆人口为155
			178万；假设每年人口的平均增长率是1%，经过20年后我国大陆人口约为172
			263.99万.
			</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			比较两种增长方式，随着时间推移，“指数增长”方式更具有爆发性.探究两种增长方式的特点，并分别列举社会生活中的“线性增长”和“指数增长”现象.
			</p>
			<p>
			一般地，形如<i>y</i>=<i>ka<sup>x</sup></i>（<i>a</i>＞0，且<i>a</i>≠1，<i>k</i>≠0）的函数称为<b>指数型函数</b>，这是生活实际中常见的和实用的函数模型.其中，当<i>a</i>＞1时，该函数叫作指数增长模型，如我们常说的“指数爆炸”现象所蕴含的就是这种模型；当0＜<i>a</i>＜1时，该函数叫作指数衰减模型，如考古工作中的碳14衰减现象所蕴含的就是这种模型.
			</p>
			<p>
			<span class="zt-ls"><b>例2</b></span>　2020年12月8日，中国、尼泊尔两国共同向全世界正式宣布，世界第一高峰珠穆朗玛峰的最新海拔高程为8
			848.86
			m.由于珠穆朗玛峰气候多变、高寒缺氧、环境复杂，对测量装备、测绘技术和测绘人员有很高的要求，因此精确测量珠穆朗玛峰高程是一个国家测绘技术水平和能力的综合体现.已知海拔高程<i>y</i>（m）
			与大气压强<i>x</i>（Pa）之间的关系可用函数 <i>y</i>=<i>k</i> ln
			<i>x</i>+<i>c</i>
			来近似描述，其中<i>c</i>，<i>k</i>可看成常量.又知登顶过程中，海平面的大气压强为1.013×10<sup>5</sup>
			Pa，北坳营地海拔7 028 m，大气压强约为4.21×10<sup>4</sup>Pa.
			</p>
			<p class="p-btn" >
			<span>
			（1）当大气压强为3.81×10<sup>4</sup> <i>Pa</i> 时，海拔高程是多少？
			</span>
			<span class="btn-box" @click="isShowAnswer53 = !isShowAnswer53">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer53" >
			<p>
			<span class="zt-ls"><b>解</b></span> 海平面的海拔高程为0 m.将
			</p>
			<p class="center">
			<i>x</i><sub>1</sub>=1.013×10<sup>5</sup>，<i>y</i><sub>1</sub>=0，
			</p>
			<p class="center">
			<i>x</i><sub>2</sub>=4.21×10<sup>4</sup>，<i>y</i><sub>2</sub>=7
			028，
			</p>
			<p>分别代入函数关系式　<i>y</i>=<i>k</i> ln <i>x</i>+<i>c</i>，</p>
			<p>解得　<i>k</i>≈-8 004.203，<i>c</i>≈92 255.180.</p>
			<p>于是，大气压强与海拔高程的关系式近似为</p>
			<math display="block">
			<mi>y</mi>
			<mo>=</mo>
			<mo>−</mo>
			<mn>8004.203</mn>
			<mi>ln</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>+</mo>
			<mn>92255.180</mn>
			<mo>.</mo>
			</math>
			<p class="right">①</p>
			<p>（1）当<i>x</i>=3.81×10<sup>4</sup>时，</p>
			<p><i>y</i>=-8 004.203×ln（3.81×10<sup>4</sup>）+92 255.180</p>
			<p>≈7 827.090.</p>
			<p>
			所以，当大气压强为3.81×10<sup>4</sup> <i>Pa</i>时，海拔高程约为7
			827.090 m.
			</p>
			</div>
			<p class="p-btn" >
			<span>
			（2）当测绘人员在登顶过程中测得其所在位置的海拔高程为8 844.43
			m时，大气压强为多少？
			</span>
			<span class="btn-box" @click="isShowAnswer54 = !isShowAnswer54">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer54" >
			<p>（2）把<i>y</i>=8 844.43代入①式，</p>
			<p class="center">8 844.43=-8 004.203 ln <i>x</i>+92 255.180，</p>
			<p class="center">
			ln <i>x</i>=10.421⇒<i>x</i>=<i>e</i><sup>10.421</sup>≈33
			556.974≈3.36×10<sup>4</sup>.
			</p>
			<p>
			所以，当测绘人员在登顶过程中测得其所在位置的海拔高程为8 844.43
			m时，大气压强约为3.36×10<sup>4</sup>
			<i>Pa</i>，约为海平面大气压强的<math display="0">
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			</math>.
			</p>
			</div>
			</div>
			</div>
			</div>
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			<div v-if="showPageList.indexOf(151) > -1">
			<ul class="page-header-odd fl al-end">
			<li>144</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			</div>
			<div class="page-box hidePage" page="151">
			</div>

			<!-- 145 -->
			<div class="page-box" page="152">
			<div v-if="showPageList.indexOf(152) > -1">

			<ul class="page-header-box">
			<li>
			<p>第四单元指数函数与对数函数</p>
			</li>
			<li>
			<p><span>145</span></p>
			<p><span>145-146</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[152] ? questionData[152][1] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			<h3 id="c047">习题4.5<span class="fontsz2">＞＞＞</span></h3>
			<div class="bj">
			<examinations :cardList="questionData[152] ? questionData[152][2] : []" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			</div>
			</div>
			</div>

			<!-- 146 -->
			<div class="page-box" page="153">
			<div v-if="showPageList.indexOf(153) > -1">
			<ul class="page-header-odd fl al-end">
			<li>146</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			</div>
			</div>

			<div class="page-box hidePage" page="153"></div>
			<!-- 147 -->
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			<div v-if="showPageList.indexOf(154) > -1">

			<ul class="page-header-box">
			<li>
			<p>第四单元指数函数与对数函数</p>
			@@ -475,10 +6450,33 @@
			<p><span>147</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<h2 id="b027">
			数学园地<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			</h2>
			<p class="center">我们身边的“指数爆炸”</p>
			<p>
			“指数爆炸”不是真正的爆炸，是事物数量的变化呈现爆炸式急剧增长时的现象.用数学语言描述该现象时，可用指数函数模型<i>f</i>（<i>x</i>）=<i>ka<sup>x</sup></i>（<i>a</i>＞1）来刻画这种变化规律，这种增长方式也叫作“指数增长”.
			</p>
			<p>
			在幼儿园、小学阶段，同学们经常玩的折纸游戏也蕴含着“指数爆炸”的道理.一张足够大、足够柔软的纸片每对折一次，纸片的厚度就会翻一番，如果持续对折下去，其厚度增长是“爆炸式”的.一张足够大的1
			mm厚的纸片如果连续对折42次，其厚度大约为4.4×10<sup>5</sup>
			km，可以直接从地球连到月球了（地球与月球之间的距离约为3.8×10<sup>5</sup>
			km）.
			</p>
			<p>
			在卫生健康方面，我们几乎每天都在和细菌打交道，因为很多细菌的繁殖速度都是呈“指数爆炸”式的.有研究显示，一双未洗过的手上大约有80万个细菌，假设某种细菌以二分裂法繁殖（每分裂一次，数量是原来的两倍），每5秒分裂一次，很快，这双未洗过的手上的细菌就会增长到5
			000多万个，庞大的细菌群体经常会导致我们“病从手入”.所以，保持饭前便后洗手的良好卫生习惯，对我们身体健康有着至关重要的作用.
			</p>
			<p>
			在旅游服务领域，一些消费性政策可能会导致游客人数的“爆炸式”增长.例如，某一景区为吸引更多游客，从2001年开始，施行门票免费活动，游客人数从30万人次增加到2020年的220万人次，平均每年增加1.11倍，这也蕴含着“指数增长”.如果游客人数增长过度，会出现景区人满为患、服务跟不上等问题，因此需要利用函数模型预测未来变化趋势，合理施行旅游活动.
			</p>
			<p>
			从细如发丝的拉面、折纸游戏、细菌繁殖，到景区旅游、银行储蓄等，都与“指数爆炸”有着千丝万缕的联系.在客观世界中，数学早已悄悄潜入我们生活、工作的方方面面.
			</p>
			</div>
			</div>
			</div>

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			<div v-if="showPageList.indexOf(155) > -1">
			@@ -487,14 +6485,173 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<h2 id="b028">
			单元小结<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			</h2>
			<p class="bj2"><b>学习导图</b></p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0159-1.jpg" />
			</p>
			<p class="bj2"><b>学习指导</b></p>
			<p>1.实数指数幂.</p>
			<p>（1）正整数、负整数、分数、指数幂的意义.</p>
			<p>
			①<math display="0">
			<msup>
			<mi>a</mi>
			<mrow>
			<mi>n</mi>
			</mrow>
			</msup>
			<mo>=</mo>
			<munder>
			<mrow data-mjx-texclass="OP">
			<munder>
			<mrow>
			<mi>a</mi>
			<mo>⋅</mo>
			<mi>a</mi>
			<mo>⋅</mo>
			<mi>a</mi>
			<mo>⋅</mo>
			<mo>⋯</mo>
			<mo>⋅</mo>
			<mi>a</mi>
			</mrow>
			<mo>⏟</mo>
			</munder>
			</mrow>
			<mrow>
			<mi>n</mi>
			<mo stretchy="false">↑</mo>
			<mi>a</mi>
			</mrow>
			</munder>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mi>n</mi>
			<mo>∈</mo>
			<msub>
			<mrow>
			<mi mathvariant="bold">N</mi>
			</mrow>
			<mrow>
			<mo>+</mo>
			</mrow>
			</msub>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>；　②<math display="0">
			<msup>
			<mi>a</mi>
			<mrow>
			<mo>−</mo>
			<mi>n</mi>
			</mrow>
			</msup>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<msup>
			<mi>a</mi>
			<mrow>
			<mi>n</mi>
			</mrow>
			</msup>
			</mfrac>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mi>a</mi>
			<mo>≠</mo>
			<mn>0</mn>
			<mo>,</mo>
			<mi>n</mi>
			<mo>∈</mo>
			<msub>
			<mrow>
			<mi mathvariant="bold">N</mi>
			</mrow>
			<mrow>
			<mo>+</mo>
			</mrow>
			</msub>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>；
			</p>
			<p>
			③<math display="0">
			<msup>
			<mi>a</mi>
			<mrow>
			<mfrac>
			<mi>m</mi>
			<mi>n</mi>
			</mfrac>
			</mrow>
			</msup>
			<mo>=</mo>
			<mroot>
			<msup>
			<mi>a</mi>
			<mrow>
			<mi>m</mi>
			</mrow>
			</msup>
			<mi>n</mi>
			</mroot>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mi>a</mi>
			<mo>></mo>
			<mn>0</mn>
			<mo>,</mo>
			<mi>m</mi>
			<mo>,</mo>
			<mi>n</mi>
			<mo>∈</mo>
			<msub>
			<mrow>
			<mi mathvariant="bold">N</mi>
			</mrow>
			<mrow>
			<mo>+</mo>
			</mrow>
			</msub>
			<mo>,</mo>
			<mi>n</mi>
			<mo>></mo>
			<mn>1</mn>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>.
			</p>
			<p>（2）运算性质.</p>
			<p>设<i>a</i>＞0，<i>b</i>＞0，<i>m</i>，<i>n</i>∈<b>R</b>，则</p>
			<p>
			①<i>a<sup>m</sup>
			a<sup>n</sup></i>=<i>a<sup>m+n</sup></i>；　②（<i>a<sup>m</sup></i>）<i><sup>n</sup></i>=<i>a<sup>mn</sup></i>；　③（<i>ab</i>）<i><sup>n</sup></i>=<i>a<sup>n</sup>
			b<sup>n</sup></i>.
			</p>
			<p>2.对数.</p>
			<p>
			（1）
			定义：如果<i>a<sup>x</sup></i>=<i>N</i>（<i>a</i>＞0，且<i>a</i>≠1），那么数<i>x</i>叫作以<i>a</i>为底<i>N</i>的<b>对数</b>，记作<i>x</i>=log<i><sub>a</sub>N</i>，其中<i>a</i>叫作对数的<b>底数</b>（简称底），<i>N</i>叫作<b>真数</b>.
			</p>
			<p>
			通常我们把log <sub>10</sub><i>N</i>叫作常用对数，简记作lg <i>N</i>；
			把log<sub>e</sub><i>N</i>叫作自然对数，简记作ln <i>N</i>.
			</p>
			<p>
			（2）性质：①零和负数没有对数；②log<i><sub>a</sub></i>1=0，即1的对数为0；③log<i><sub>a</sub>a</i>=1，即底数的对数为1.
			</p>
			</div>
			</div>
			</div>

			<!-- 149 -->
			<div class="page-box" page="156">
			<div v-if="showPageList.indexOf(156) > -1">

			<ul class="page-header-box">
			<li>
			<p>第四单元指数函数与对数函数</p>
			@@ -503,69 +6660,300 @@
			<p><span>149</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p>（3）运算法则.</p>
			<p>
			①log<i><sub>a</sub></i>（<i>MN</i>）=log<i><sub>a</sub>M</i>+log<i><sub>a</sub>N</i>；　②<math display="0">
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>M</mi>
			<mi>N</mi>
			</mfrac>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>M</mi>
			<mo>−</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>N</mi>
			</math>；
			</p>
			<p>
			③log<i><sub>a</sub>N<sup>n</sup></i>=<i>n</i>log
			<i><sub>a</sub>N</i>（<i>a</i>＞0，且<i>a</i>≠1，<i>n</i>∈<b>R</b>）.
			</p>
			<p>（4）（选学）换底公式.</p>
			<p>
			<math display="0">
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>b</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>c</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>b</mi>
			</mrow>
			<mrow>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>c</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>a</mi>
			</mrow>
			</mfrac>
			</math>（<i>a</i>＞0，且<i>a</i>≠1；<i>c</i>＞0，且<i>c</i>≠1）.
			</p>
			<p>
			特别地，<math display="0">
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>b</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>b</mi>
			</mrow>
			<mrow>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>a</mi>
			</mrow>
			</mfrac>
			</math>（<i>a</i>＞0，且<i>a</i>≠1）.
			</p>
			<p>
			对数恒等式：<math display="0">
			<msup>
			<mi>a</mi>
			<mrow>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>N</mi>
			</mrow>
			</msup>
			<mo>=</mo>
			<mi>N</mi>
			</math>（<i>a</i>＞0，且<i>a</i>≠1）.
			</p>
			<p>3.指数函数与对数函数.</p>
			<p>（1）定义.</p>
			<p>
			形如<i>y</i>=<i>a<sup>x</sup></i>（<i>a</i>＞0，且<i>a</i>≠1）的函数叫指数函数；形如<i>y</i>=log<i>
			ax</i>（<i>a</i>＞0，且<i>a</i>≠1）的函数叫对数函数.
			</p>
			<p>（2）图像和性质.</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0160-5.jpg" />
			</p>
			<p>4.指数函数与对数函数的实际应用.</p>
			<p>
			分析实例背景，建立指数函数或对数函数模型，并利用指数函数、对数函数的图像及基本性质解决简单的实际问题.体会“指数爆炸”与“指数衰减”的特点.
			</p>
			</div>
			</div>
			</div>

			<!-- 150 -->
			<div class="page-box" page="157">
			<div v-if="showPageList.indexOf(157) > -1">
			<ul class="page-header-odd fl al-end">
			<li>150</li>
			<li>150-152</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<h2 id="b029">
			单元检测<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			</h2>
			<div class="bj">
			<examinations :cardList="questionData[157]" :hideCollect="true" sourceType="json" inputBc="#d3edfa" v-if="questionData">
			</examinations>
			</div>
			</div>
			</div>
			</div>
			<!-- 151 -->
			<div class="page-box" page="158">
			<div v-if="showPageList.indexOf(158) > -1">

			<ul class="page-header-box">
			<li>
			<p>第四单元指数函数与对数函数</p>
			</li>
			<li>
			<p><span>151</span></p>
			</li>
			</ul>
			<div class="padding-116">158</div>
			</div>
			</div>
			<div class="page-box hidePage" page="158"></div>
			<!-- 152 -->
			<div class="page-box" page="159">
			<div v-if="showPageList.indexOf(159) > -1">
			<ul class="page-header-odd fl al-end">
			<li>152</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116">159</div>
			<div class="page-box hidePage" page="159"></div>
			<!-- 解题思路弹窗 -->
			<el-dialog :visible.sync="thinkingDialog" width="40%" :append-to-body="true" :show-close="false"
			@close="closeDialog" class="thinkDialog">
			<div slot="title" class="think-header"
			style="padding: 0; text-align: center; color: #333;display:flex;justify-content: center;">
			<span style=""> 分析 </span>
			<svg style="position: absolute; right:10px;cursor: pointer;" @click="thinkingDialog = false" t="1718596022986"
			class="icon" viewBox="0 0 1024 1024" version="1.1" xmlns="http://www.w3.org/2000/svg" p-id="4252" width="20"
			height="20" xmlns:xlink="http://www.w3.org/1999/xlink">
			<path
			d="M176.661601 817.172881C168.472798 825.644055 168.701706 839.149636 177.172881 847.338438 185.644056 855.527241 199.149636 855.298332 207.338438 846.827157L826.005105 206.827157C834.193907 198.355983 833.964998 184.850403 825.493824 176.661601 817.02265 168.472798 803.517069 168.701706 795.328267 177.172881L176.661601 817.172881Z"
			fill="#979797" p-id="4253"></path>
			<path
			d="M795.328267 846.827157C803.517069 855.298332 817.02265 855.527241 825.493824 847.338438 833.964998 839.149636 834.193907 825.644055 826.005105 817.172881L207.338438 177.172881C199.149636 168.701706 185.644056 168.472798 177.172881 176.661601 168.701706 184.850403 168.472798 198.355983 176.661601 206.827157L795.328267 846.827157Z"
			fill="#979797" p-id="4254"></path>
			</svg>
			</div>
			</div>
			<ul>
			<li v-for="(item, index) in thinkData" :key="index">
			<div v-if="index <= showIndex" style="display: flex">
			<span style="position: relative">
			<span style="position: absolute; top: 16px; left: 13px; color: #fff">{{ index + 1 }}</span>
			<img src="../../assets/images/icon/blue-group.png" alt="" style="margin-right: 10px"
			v-if="index < thinkOne.length - 1" />
			<img src="../../assets/images/icon/blue.png" alt="" v-if="index == thinkOne.length - 1"
			style="margin-right: 10px" />
			</span>
			<p class="txt-p" v-html="item"></p>
			</div>
			</li>
			</ul>
			<div @click="changeNext" style="
			display: flex;
			flex-direction: column;
			align-items: center;
			justify-content: center;
			">
			<img src="../../assets/images/icon/mouse.png" alt="" v-if="showIndex < thinkData.length - 1" />
			<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" t="1710234570135"
			class="icon" viewBox="0 0 1024 1024" version="1.1" p-id="5067" width="15" height="15">
			<path
			d="M2.257993 493.371555 415.470783 906.584344 512 1003.113561 608.529217 906.584344 1021.742007 493.371555 925.212789 396.842337 512 810.055127 98.787211 396.842337Z"
			fill="#1296db" p-id="5068" />
			<path
			d="M2.257993 117.980154 415.470783 531.192944 512 627.722161 608.529217 531.192944 1021.742007 117.980154 925.212789 21.450937 512 434.663727 98.787211 21.450937Z"
			fill="#1296db" p-id="5069" />
			</svg>
			</div>
			</el-dialog>
			</div>
			</template>

			<script>
			import examinations from "@/components/examinations/index.vue";
			const handleShow = (num) => {
			const obj = {}
			for (let index = 0; index < num; index++) {
			obj['isShowAnswer' + index] = false
			}
			return obj
			}
			const showObj = handleShow(60)
			export default {
			name: '',
			name: "",
			props: {
			showPageList: {
			type: Array,
			default: [],
			},
			questionData: {
			type: Object,
			},
			},
			components: {},
			components: { examinations },
			data() {
			return {}
			return {
			...showObj,
			showIndex:0,
			thinkingDialog: false,
			thinkData:[],
			thinkOne:[
			'运算思路是将根式转化为分数指数幂，然后再化简运算.'
			]
			,
			thinkTwo:[
			'观察这个式子的特点，每一项都是前面一项的2倍（除第1项外）；',
			'运算思路可考虑将代数式每项乘2后再与原式相减.数学上把这种运算方法叫作“错位相减”.'
			],
			thinkThree:[
			'1.8<sup>2.5</sup>和1.8<sup>3</sup>分别可以看作<i>y</i>=1.8<i><sup>x</sup></i>在<i>x</i>=2.5和<i>x</i>=3处的函数值，这样就可以利用函数的单调性来比较函数值的大小.0.9<sup>-0.2</sup>和0.9<sup>-0.3</sup>分别可以看作<i>y</i>=0.9<i><sup>x</sup></i>在<i>x</i>=-0.2和<i>x</i>=-0.3处的函数值，同样可以利用函数的单调性来比较函数值的大小.'
			],
			thinkFour:[
			'利用性质“1的对数为0”和“底数的对数为1” 直接得答案，不必转化成指数式.'
			],
			thinkFive:[
			'利用对数运算性质进行化简运算.'
			],
			thinkSix:[
			'首先根据条件确定底数<i>a</i>，然后再计算对应函数值.'
			],
			thinkSeven:[
			'若两个对数的底数相同，可利用对数函数的单调性直接比较；若底数不同，可采用先与中间量（通常是0或1）进行比较，再利用不等式传递性得出结论.'
			],
			thinkEight:[
			'（1）这是经济社会中的“线性增长”现象，即每年增加量保持不变，每年增加700万人口，20年共增加14000万人口，因此总共人口为155 178万.'
			],
			thinkNine:[
			' 这是经济社会中的“指数增长”现象，即每年按照一定的增长率（成倍数）增长.我们首先考查逐年增长的情况，从中发现每一年都是前一年的（1+1%）倍（也可采用后一年与前一年的比值发现规律），即呈指数增长，最后利用指数函数知识解决问题.',
			'2020年年末人口约为141 178万；',
			'经过1年人口约为141 178（1+1%）万；',
			'经过2年人口约为141 178（1+1%）（1+1%）=141 178（1+1%）<sup>2</sup>万；',
			'经过3年人口约为141 178（1+1%）<sup>2</sup>（1+1%）=141 178（1+1%）<sup>3</sup>万；',
			'经过<i>x</i>年人口约为141 178（1+1%）<i><sup>x</sup></i>万.'

			]
			};
			},
			computed: {},
			watch: {},
			created() { },
			mounted() { },
			methods: {},
			}
			methods: {
			openDialog(queryData) {
			this.thinkData = queryData
			this.thinkingDialog = !this.thinkingDialog
			},
			closeDialog() {
			this.showIndex = 0
			},
			changeNext() {
			if (this.showIndex < this.thinkData.length - 1) this.showIndex = this.showIndex + 1
			}
			},
			};
			</script>

			<style lang="less" scoped></style>
			<style lang="less" scoped>
			li {
			list-style: none;
			}
			</style>