数学

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2024-10-16 d7bb63ff28f0f08f377239139893fa5b263c844f

 src/books/mathBook/view/components/chapter004.vue

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            <img class="img-b" alt="" src="../../assets/images/0149-1.jpg" />
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          <p class="img">图4-8</p>
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          <p class="img">图4-9</p>
          <p><b>类比归纳</b></p>
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            <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>
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                <mo data-mjx-texclass="NONE">⁡</mo>
                <mi>x</mi>
              </math>的图像有什么关系？
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            <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.
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          <p>
            <span class="zt-ls"><b>例1</b></span>　比较下列各组数中两个值的大小.
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            <p>第四单元 指数函数与对数函数</p>
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            <p><span>141</span></p>
            <p><span>141-142</span></p>
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        <ul class="page-header-odd fl al-end">
          <li>142</li>
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
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            <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？
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          <h2 id="b026">
            4.5 指数函数与对数函数的实际应用<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
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          <h3 id="c047">习题4.5<span class="fontsz2">＞＞＞</span></h3>
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            单元检测<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
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