testbookLayout.git

			@@ -1,5 +1,5 @@
			<template>
			<div class="chapter" num="4">
			<div class="chapter" num="5">
			<!-- 第四单元首页 -->
			<div class="page-box" page="120">
			<div v-if="showPageList.indexOf(120) > -1">
			@@ -335,67 +335,29 @@
			<p>
			<span class="zt-ls"><b>例1</b></span>　计算.
			</p>
			<p>
			（1）
			<math display="0">
			<mroot>
			<msup>
			<mn>5</mn>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mn>3</mn>
			</mroot>
			</math>；（2）
			<math display="0">
			<mroot>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<p class="p-btn" >
			<span>（1）
			<math display="0">
			<mroot>
			<msup>
			<mn>5</mn>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mn>3</mn>
			</mroot>
			</math>；（3）
			<math display="0">
			<mroot>
			<msup>
			<mn>7</mn>
			<mrow>
			<mn>4</mn>
			</mrow>
			</msup>
			<mn>4</mn>
			</mroot>
			</math>；
			<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>
			（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>；（5） 81的4次方根.
			</p>
			<p>
			<p v-if="isShowAnswer0" >
			<span class="zt-ls"><b>解</b></span>（1）<math display="0">
			<mroot>
			<msup>
			@@ -410,7 +372,36 @@
			<mn>5</mn>
			</math>；
			</p>
			<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>
			@@ -432,7 +423,31 @@
			<mn>5</mn>
			</math>；
			</p>
			<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>
			@@ -452,7 +467,36 @@
			<mn>7</mn>
			</math>；
			</p>
			<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>
			@@ -480,7 +524,18 @@
			<mn>7</mn>
			</math>；
			</p>
			<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>
			@@ -495,46 +550,36 @@
			<p>
			<span class="zt-ls"><b>例2</b></span>　化简.
			</p>
			<p>
			（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>；（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>
			<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>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>4</mn>
			</mrow>
			</msup>
			<mn>4</mn>
			</mroot>
			</math>.
			<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>
			<p v-if="isShowAnswer5" >
			<span class="zt-ls"><b>解</b></span>（1）
			<math display="0">
			<mroot>
			@@ -558,7 +603,39 @@
			<mi>a</mi>
			</math>；
			</p>
			<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>
			@@ -885,46 +962,30 @@
			<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>
			（1）
			<math display="0">
			<mroot>
			<msup>
			<mi>a</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mn>4</mn>
			</mroot>
			</math>；（2）
			<math display="0">
			<mroot>
			<msup>
			<mi>x</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mn>6</mn>
			</mroot>
			</math>；（3）
			<math display="0">
			<mfrac>
			<mn>1</mn>
			<p class="p-btn" >
			<span>
			（1）
			<math display="0">
			<mroot>
			<msup>
			<mn>5</mn>
			<mi>a</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mn>4</mn>
			</mroot>
			</mfrac>
			</math>.
			</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>
			<p v-if="isShowAnswer7" >
			<span class="zt-ls"><b>解</b></span>（1）
			<math display="0">
			<mroot>
			@@ -948,8 +1009,31 @@
			</msup>
			</math>；
			</p>
			<p>
			（2）
			<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>
			@@ -982,8 +1066,34 @@
			</msup>
			</math>）
			</p>
			<p>
			（3）
			<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>
			@@ -1026,51 +1136,30 @@
			<p>
			<span class="zt-ls"><b>例4</b></span>　化简（式中字母均为正实数）.
			</p>
			<p>
			（1）<math display="0">
			<msup>
			<mn>27</mn>
			<mrow>
			<mo>−</mo>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			</mrow>
			</msup>
			</math>；（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>.
			<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>
			<p v-if="isShowAnswer10" >
			<span class="zt-ls"><b>解</b></span>（1）<math display="0">
			<msup>
			<mn>27</mn>
			@@ -1110,8 +1199,50 @@
			</mfrac>
			</math>；
			</p>
			<p>
			（2）<math display="0">
			<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>
			@@ -1337,7 +1468,7 @@
			<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">
			@@ -1355,284 +1486,313 @@
			<p>
			<span class="zt-ls"><b>例1</b></span>　计算（式中字母均为正实数）.
			</p>
			<p>
			（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>
			<p class="p-btn" >
			<span>
			（1）<math display="0">
			<msup>
			<mfrac>
			<mn>1</mn>
			<mn>27</mn>
			</mfrac>
			<mn>16</mn>
			<mrow>
			<mo>−</mo>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			<mn>4</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>；（2）
			<math display="0">
			<msup>
			<mo>−</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mi>a</mi>
			<mfrac>
			<mn>1</mn>
			<mn>27</mn>
			</mfrac>
			<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>1</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>.
			</p>
			<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>
			<mo>+</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">（</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>
			<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>
			</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>
			</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>
			<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>
			<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>
			@@ -1838,85 +1998,52 @@
			</mtable>
			</math>
			</p>
			<p>
			<span class="zt-ls"><b>例2</b></span>　化简（式中字母均为正实数）.
			<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>
			（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>；（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>.
			<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>
			<p class="block">
			<span class="zt-ls2"><b>分析</b></span>　运算思路是将根式转化为分数指数幂，然后再化简运算.
			</p>
			<p>
			<span class="zt-ls"><b>解</b></span>
			</p>
			<math display="">
			<mtable columnalign="left" columnspacing="1em" rowspacing="4pt">
			<mtr>
			<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>
			@@ -2054,6 +2181,72 @@
			<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>
			@@ -2307,135 +2500,137 @@
			</mtr>
			</mtable>
			</math>
			</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">
			<p>
			<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>）.
			<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>
			<p class="block">
			<span
			class="zt-ls2"><b>分析</b></span>　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”.
			</p>
			<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>
			<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>
			</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>
			<mrow>
			<mn>0</mn>
			</mrow>
			</msup>
			<mo>+</mo>
			<msup>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo>+</mo>
			<msup>
			<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>
			<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>
			<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>
			@@ -2445,6 +2640,9 @@
			</div>
			</div>
			</div>
			</div>
			<!-- 120 -->
			<div class="page-box hidePage" page="127">
			</div>
			<!-- 121 -->
			<div class="page-box" page="128">
			@@ -2641,26 +2839,46 @@
			<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>（1）求函数<i>f</i>（<i>x</i>）的解析式；</p>
			<p>
			（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.
			<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>
			<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>
			（2）
			<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>
			@@ -2952,8 +3170,17 @@
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0136-1.jpg" />
			</p>
			<p>
			<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.
			<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>.
			@@ -2971,14 +3198,17 @@
			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>
			<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 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">
			@@ -2995,7 +3225,7 @@
			<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>
			@@ -3003,266 +3233,346 @@
			<p>
			<span class="zt-ls"><b>例2</b></span>　判断下列函数在（-∞，+∞）内的单调性.
			</p>
			<p>
			（1） <i>y</i>=4<i><sup>x</sup></i>；（2） <i>y</i>=3<i><sup>-x</sup></i>；（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>.
			<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>
			<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>
			（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>
			（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>
			<ul class="fl">
			<li>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0137-7.jpg" />
			<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>
			</li>
			<li>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0137-8.jpg" />
			</p>
			<p class="img">图4-6</p>
			</li>
			<li>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0137-9.jpg" />
			</p>
			<p class="img">图4-7</p>
			</li>
			</ul>
			<p>
			<span class="zt-ls"><b>例3</b></span>　比较下列各题中两个值的大小.
			</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>
			<p>
			（1） 1.8<sup>2.5</sup>与1.8<sup>3</sup>；（2）
			0.9<sup>-0.2</sup>与0.9<sup>-0.3</sup>.
			</p>
			<p class="block">
			<span
			class="zt-ls2"><b>分析</b></span>　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.
			</p>
			<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>
			<p>
			（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>
			<p>
			<span class="zt-ls"><b>例4</b></span>　求函数<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msqrt>
			<div v-if="isShowAnswer21" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			（2）
			<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msup>
			<mn>2</mn>
			<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>
			<mn>4</mn>
			</msqrt>
			</math>的定义域.
			<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>
			<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.
			<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>故函数的定义域为2，+∞）.</p>
			</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">
			<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>
			（1）求<i>f</i>（-1）的值；（2）
			若<i>f</i>（m）≥9，求<i>m</i>的取值范围.
			<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>
			<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>
			<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>
			</msup>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>3</mn>
			</mfrac>
			</math>.
			<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>
			<p>
			（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 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>
			@@ -3273,7 +3583,9 @@
			</div>
			</div>
			</div>

			<!-- 127 -->
			<div class="page-box hidePage" page="134">
			</div>
			<!-- 128 -->
			<div class="page-box" page="135">
			<div v-if="showPageList.indexOf(135) > -1">
			@@ -3291,7 +3603,6 @@
			</div>
			</div>
			</div>

			<!-- 129 -->
			<div class="page-box" page="136">
			<div v-if="showPageList.indexOf(136) > -1">
			@@ -3353,7 +3664,6 @@
			</div>
			</div>
			</div>

			<!-- 130 -->
			<div class="page-box" page="137">
			<div v-if="showPageList.indexOf(137) > -1">
			@@ -3389,8 +3699,17 @@
			<examinations :cardList="questionData[137]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			<p>
			<span class="zt-ls"><b>例1</b></span>　把下列指数式写成对数式.
			<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）
			@@ -3408,7 +3727,7 @@
			<mn>16</mn>
			</math>；（3） 10<sup>-2</sup>=0.01.
			</p>
			<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>
			@@ -3425,8 +3744,17 @@
			</mfrac>
			</math>；（3） lg0.01=-2.
			</p>
			<p>
			<span class="zt-ls"><b>例2</b></span>　把下列对数式写成指数式.
			<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）
			@@ -3448,7 +3776,7 @@
			<mn>3</mn>
			</math>；（3） <i>ln</i>1=0.
			</p>
			<p>
			<p v-if="isShowAnswer29" >
			<span class="zt-ls"><b>解</b></span>（1） 3<sup>5</sup>=243；（2）
			<math display="0">
			<msup>
			@@ -3471,8 +3799,17 @@
			</mfrac>
			</math>；（3） <i>e</i><sup>0</sup>=1.
			</p>
			<p>
			<span class="zt-ls"><b>例3</b></span>　求下列各式中<i>N</i>的值.
			<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）
			@@ -3491,93 +3828,124 @@
			</mfrac>
			</math>.
			</p>
			<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>
			<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>
			</mrow>
			</msup>
			<mo>=</mo>
			<mn>4</mn>
			</math>.
			</p>
			<p>
			<span class="zt-ls"><b>例4</b></span>　求下列各式中<i>x</i>的值.
			<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>
			<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>
			<p>
			<span class="zt-ls"><b>例5</b></span>　求下列各式的值.
			<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>
			<p>
			<span class="zt-ls2"><b>分析</b></span>　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
			</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">
			@@ -3590,11 +3958,6 @@
			</li>
			</ul>
			<div class="padding-116">
			<p>数式.</p>
			<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>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			@@ -3618,7 +3981,6 @@
			</div>
			</div>
			</div>

			<!-- 132 -->
			<div class="page-box" page="139">
			<div v-if="showPageList.indexOf(139) > -1">
			@@ -3718,159 +4080,165 @@
			<examinations :cardList="questionData[139]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			<p>
			<span
			<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>
			（1） log<i><sub>a</sub></i>（<i>x</i><sup>2</sup><i>yz</i><sup>3</sup>）；（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>
			<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>
			<mn>2</mn>
			<mi>a</mi>
			</mrow>
			</msup>
			<mrow>
			<mi>y</mi>
			<mi>z</mi>
			</mrow>
			</mfrac>
			</math>；（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>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mi>y</mi>
			<mi>x</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mi>z</mi>
			<mi>y</mi>
			<msup>
			<mi>z</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</mfrac>
			</math>.
			</p>
			<p class="block">
			<span class="zt-ls2"><b>分析</b></span>　利用对数运算性质进行化简运算.
			</p>
			<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>
			<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 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>
			<mo>=</mo>
			<mn>2</mn>
			<msub>
			<mi>log</mi>
			<mrow>
			<mi>a</mi>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<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>
			<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>
			<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>
			<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">
			<p class="left1" v-if="isShowAnswer34">
			<math display="">
			<mo stretchy="false">（2）</mo>
			<msub>
			@@ -3981,7 +4349,42 @@
			<mo>;</mo>
			</math>
			</p>
			<p class="left1">
			<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>
			@@ -4073,111 +4476,117 @@
			<p>
			<span class="zt-ls"><b>例2</b></span>　计算.
			</p>
			<p>
			（1）
			<math display="0">
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>5</mn>
			</mrow>
			</msub>
			<mroot>
			<mn>25</mn>
			<mn>3</mn>
			</mroot>
			</math>；（2） log <sub>3</sub>（9<sup>3</sup>×3<sup>5</sup>）；（3） log
			<sub>7</sub>56-log<sub>7</sub>8.
			<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>
			</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>
			</li>
			<li>
			<p><span>133</span></p>
			</li>
			</ul>

			<div class="padding-116">
			<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>
			<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>
			<mn>2</mn>
			<mfrac>
			<mn>2</mn>
			<mn>3</mn>
			</mfrac>
			</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>
			<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>
			<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>
			<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 class="left1">
			<p v-if="isShowAnswer37" class="left1">
			<math display="">
			<mo stretchy="false">（2）</mo>
			<msub>
			@@ -4269,7 +4678,20 @@
			<mo>;</mo>
			</math>
			</p>
			<p class="left1">
			<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>
			@@ -4315,11 +4737,30 @@
			<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>
			</li>
			<li>
			<p><span>133</span></p>
			</li>
			</ul>

			<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" v-if="questionData">
			<examinations :cardList="questionData[140]" :hideCollect="true" sourceType="json" inputBc="#d3edfa" v-if="questionData">
			</examinations>
			</div>
			<h3 id="c042">
			@@ -4522,7 +4963,6 @@
			</div>
			</div>
			</div>

			<!-- 134 -->
			<div class="page-box" page="141">
			<div v-if="showPageList.indexOf(141) > -1">
			@@ -4532,272 +4972,183 @@
			<li>上册</li>
			</ul>
			<div class="padding-116">
			<p>
			<span class="zt-ls"><b>例1</b></span>　求log<sub>27</sub>8·log <sub>32</sub>9的值.
			<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>
			<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>
			<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>
			</msup>
			</mrow>
			<mrow>
			<mi>lg</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<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>
			<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>
			</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>
			</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>
			<p>
			<span
			</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>
			<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>
			<div v-if="isShowAnswer40" >
			<p>
			<b>证明</b>
			<math display="0">
			<msub>
			<mi>log</mi>
			<mrow>
			@@ -4805,25 +5156,145 @@
			</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>
			<p>
			<span class="zt-ls"><b>例3</b></span>　求下列各式的值.
			<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）
			@@ -4872,170 +5343,172 @@
			</msup>
			</math>.
			</p>
			<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>
			<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>
			<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>
			<mrow>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>7</mn>
			<mrow>
			</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>
			</msup>
			</mrow>
			</msup>
			<mo>=</mo>
			<msup>
			<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>
			<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>
			<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>
			@@ -5046,7 +5519,6 @@
			</div>
			</div>
			</div>

			<!-- 135 -->
			<div class="page-box" page="142">
			<div v-if="showPageList.indexOf(142) > -1">
			@@ -5080,7 +5552,6 @@
			</div>
			</div>
			</div>

			<!-- 136 -->
			<div class="page-box" page="143">
			<div v-if="showPageList.indexOf(143) > -1">
			@@ -5147,100 +5618,139 @@
			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>
			<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>
			<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 data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>的值.
			</p>
			<p class="block">
			<span class="zt-ls2"><b>分析</b></span>　首先根据条件确定底数<i>a</i>，然后再计算对应函数值.
			</p>
			<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>
			<mo>=</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<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>
			<mrow>
			<mo>−</mo>
			<mn>3</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<mo>−</mo>
			<mn>3</mn>
			<mrow>
			<mo>−</mo>
			<mn>3</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<mo>−</mo>
			<mn>3</mn>
			</math>.
			</p>
			</math>.
			</p>
			</div>
			<p>
			<span class="zt-ls"><b>例2</b></span>　求下列函数的定义域.
			</p>
			<p>
			（1） <i>y</i>=log <sub>0.5</sub>（<i>x</i>-3）；（2）
			<i>y</i>=log<sub>3</sub>（4-<i>x</i><sup>2</sup>）.
			<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>
			<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.
			<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>
			<p>
			所以，<i>y</i>=log <sub>0.5</sub>（<i>x</i>-3）的定义域是（3，+∞）.
			</p>
			<p>
			（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 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">
			@@ -5258,7 +5768,7 @@
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[144]" :hideCollect="true" sourceType="json" v-if="questionData">
			<examinations :cardList="questionData[144]" :hideCollect="true" sourceType="json" inputBc="#d3edfa" v-if="questionData">
			</examinations>
			</div>
			<h3 id="c045">
			@@ -5328,7 +5838,6 @@
			</div>
			</div>
			</div>

			<!-- 138 -->
			<div class="page-box" page="145">
			<div v-if="showPageList.indexOf(145) > -1">
			@@ -5339,11 +5848,11 @@
			</ul>
			<div class="padding-116">
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0149-1.jpg" />
			<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-c" alt="" src="../../assets/images/0149-2.jpg" />
			<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>
			@@ -5410,7 +5919,6 @@
			</div>
			</div>
			</div>

			<!-- 139 -->
			<div class="page-box" page="146">
			<div v-if="showPageList.indexOf(146) > -1">
			@@ -5433,55 +5941,103 @@
			<img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
			</p>
			</div>
			<p class="block">
			1.你还能从图4-10中观察发现其他共性特征吗？比如，对数函数<i>y</i>=log
			2<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>的图像有什么关系？
			</p>
			<p class="block">
			2.两人一组，一人用表格呈现指数函数的图像与性质，另一人用表格呈现对数函数的图像与性质，然后对比两个函数的图像与性质，归纳总结为一个表格，并与同学交流分享.
			</p>
			<examinations :cardList="questionData[146]" :hideCollect="true" sourceType="json"
			v-if="questionData" ></examinations>
			</div>
			<p>
			<span class="zt-ls"><b>例1</b></span>　比较下列各组数中两个值的大小.
			<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>
			（1） log<sub>2</sub>5.3 与log<sub>2</sub>4.7；（2） log
			<sub>0.2</sub>7与log <sub>0.2</sub>9；
			<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>
			<p>
			（3） log<sub>5</sub>4与1；（4）log<sub>3</sub>4与log
			<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>
			<p class="block">
			<span class="zt-ls2"><b>分析</b></span>　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.
			</p>
			<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>
			（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>
			</div>
			</div>
			</div>

			<!-- 140 -->
			<div class="page-box" page="147">
			<div v-if="showPageList.indexOf(147) > -1">
			@@ -5492,149 +6048,153 @@
			</ul>
			<div class="padding-116">
			<p>
			（3） log<sub>5</sub>4＜log<sub>5</sub>5=1，即log<sub>5</sub>4＜1.
			</p>
			<ul class="fl">
			<li>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0151-1.jpg" />
			</p>
			<p class="img">图4-10</p>
			</li>
			<li>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0151-2.jpg" />
			</p>
			<p class="img">图4-11</p>
			</li>
			</ul>
			<p>
			（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>
			<p>
			<span class="zt-ls"><b>例2</b></span>　解下列不等式.
			</p>
			<p>
			（1）log <sub>4</sub><i>x</i>＜log<sub>4</sub>5；（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>.
			<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>
			<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.
			<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>
			<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>
			<p>
			（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>
			<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>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>）.
			</p>
			</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>
			@@ -5645,7 +6205,6 @@
			</div>
			</div>
			</div>

			<!-- 141 -->
			<div class="page-box" page="148">
			<div v-if="showPageList.indexOf(148) > -1">
			@@ -5654,7 +6213,7 @@
			<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">
			@@ -5662,95 +6221,6 @@
			<div class="bj">
			<examinations :cardList="questionData[148]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			</div>
			</div>
			</div>

			<!-- 142 -->
			<div class="page-box" page="149">
			<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 class="bj">
			<p>A.（0，1）</p>
			<p>B.（1，2）</p>
			<p>C.（1，+∞）</p>
			<p>D.（0，2）</p>
			<p>
			（3）函数<i>y</i>=3+log<i><sub>a</sub>x</i>（<i>a</i>＞0，且<i>a</i>≠1）的图像过定点（　）.
			</p>
			<p>A.（0，1）</p>
			<p>B.（1，0）</p>
			<p>C.（1，3）</p>
			<p>D.（1，4）</p>
			<p>
			（4）已知log<sub>0.5</sub><i>x</i>＞log<sub>0.5</sub>3，则<i>x</i>的取值范围是（　）.
			</p>
			<p>A.（3，+∞）</p>
			<p>B.（0，+∞）</p>
			<p>C.（-∞，3）</p>
			<p>D.（0，3）</p>
			<p>
			（5）
			已知<i>a</i>=log<sub>0.7</sub>0.8，<i>b</i>=log<sub>0.7</sub>1.9，<i>c</i>=log<sub>5</sub>1，则<i>a</i>，<i>b</i>，<i>c</i>的大小关系是（　）.
			</p>
			<p>A.<i>a</i>＜<i>b</i>＜<i>c</i></p>
			<p>B.<i>a</i>＜<i>c</i>＜<i>b</i></p>
			<p>C.<i>b</i>＜<i>a</i>＜<i>c</i></p>
			<p>D.<i>b</i>＜<i>c</i>＜<i>a</i></p>
			<p>2.求下列函数的定义域.</p>
			<p>
			（1）
			<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<mfrac>
			<mi>x</mi>
			<msqrt>
			<mn>1</mn>
			<mo>−</mo>
			<msub>
			<mi>log</mi>
			<mrow>
			<mn>3</mn>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			</msqrt>
			</mfrac>
			</math>；（2）
			<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<msqrt>
			<msub>
			<mi>log</mi>
			<mrow>
			<mfrac>
			<mn>1</mn>
			<mn>4</mn>
			</mfrac>
			</mrow>
			</msub>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			</msqrt>
			</math>.
			</p>
			<p>
			3.已知函数<i>f</i>（<i>x</i>）=log<i><sub>a</sub>x</i>（<i>a</i>＞0，且<i>a</i>≠1）的图像过点（9，-2），求<i>f</i>（3）的值.
			</p>
			<p>
			4.我国经济总量占世界经济的比重达18.5%，居世界第二位.2020年我国全年<i>GDP</i>为1
			015
			986亿元，取得了超过100万亿的历史性成就.2021年我国<i>GDP</i>预期目标是增长率超过6.0%.假设我国每年<i>GDP</i>的增长率均为6.0%，从2021年开始，大约经过多少年，我国能实现全年<i>GDP</i>比2021年翻一番？
			</p>
			</div>
			<h2 id="b026">
			4.5 指数函数与对数函数的实际应用<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			@@ -5764,13 +6234,35 @@
			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>
			（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？
			<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>

			<!-- 142 -->
			<div class="page-box hidePage" page="149">
			</div>
			<!-- 143 -->
			<div class="page-box" page="150">
			<div v-if="showPageList.indexOf(150) > -1">
			@@ -5779,52 +6271,43 @@
			<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">
			<p>
			（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）
			<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>
			<p class="block">
			<b>分析</b>（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14
			000万人口，因此总共人口为155 178万.
			</p>
			<p class="block">
			（2）
			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.
			</p>
			<p class="block">2020年年末人口约为141 178万；</p>
			<p class="block">经过1年人口约为141 178（1+1%）万；</p>
			<p class="block">
			经过2年人口约为141 178（1+1%）（1+1%）=141
			178（1+1%）<sup>2</sup>万；
			</p>
			<p class="block">
			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；
			</p>
			<p class="block">……</p>
			<p class="block">
			经过<i>x</i>年人口约为141 178（1+1%）<i><sup>x</sup></i>万.
			</p>
			<p>
			<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>
			<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 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>
			@@ -5834,18 +6317,6 @@
			<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>
			</div>
			</div>
			</div>
			<!-- 144 -->
			<div class="page-box" page="151">
			<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">
			<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
			@@ -5855,66 +6326,90 @@
			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>
			<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>
			<p>
			（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？
			<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>
			<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>
			<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 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>

			<!-- 144 -->
			<div class="page-box hidePage" page="151">
			</div>
			<!-- 145 -->
			<div class="page-box" page="152">
			<div v-if="showPageList.indexOf(152) > -1">
			@@ -5927,18 +6422,23 @@
			</li>
			</ul>
			<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]" :hideCollect="true" sourceType="json" v-if="questionData">
			<examinations :cardList="questionData[152] ? questionData[152][2] : []" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			</div>
			</div>
			</div>

			<!-- 146 -->
			<div class="page-box hidePage" page="153"></div>

			<!-- 147 -->
			<div class="page-box" page="154">
			<div v-if="showPageList.indexOf(154) > -1">
			@@ -5977,7 +6477,6 @@
			</div>
			</div>
			</div>

			<!-- 148 -->
			<div class="page-box" page="155">
			<div v-if="showPageList.indexOf(155) > -1">
			@@ -6150,7 +6649,6 @@
			</div>
			</div>
			</div>

			<!-- 149 -->
			<div class="page-box" page="156">
			<div v-if="showPageList.indexOf(156) > -1">
			@@ -6298,7 +6796,6 @@
			</div>
			</div>
			</div>

			<!-- 150 -->
			<div class="page-box" page="157">
			<div v-if="showPageList.indexOf(157) > -1">
			@@ -6312,7 +6809,7 @@
			单元检测<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			</h2>
			<div class="bj">
			<examinations :cardList="questionData[157]" :hideCollect="true" sourceType="json" v-if="questionData">
			<examinations :cardList="questionData[157]" :hideCollect="true" sourceType="json" inputBc="#d3edfa" v-if="questionData">
			</examinations>
			</div>
			</div>
			@@ -6322,11 +6819,68 @@
			<div class="page-box hidePage" page="158"></div>
			<!-- 152 -->
			<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>
			<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: "",
			props: {
			@@ -6340,11 +6894,66 @@
			},
			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.'

			]
			};
			},
			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>