Bài 5: Phương trình mũ và phương trình lôgarit
<span data-v-a7c68f28="">Hướng dẫn giải Bài 1 (Trang 84 SGK Toán Giải Tích 12)</span>
<p><strong>Bài 1 (Trang 84 SGK Toán Giải Tích 12):</strong></p>
<p>Giải các phương trình mũ:</p>
<p>a) <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>0</mn><mo>,</mo><mn>3</mn></mrow></mfenced><mrow><mn>3</mn><mi>x</mi><mo>-</mo><mn>2</mn></mrow></msup><mo> </mo><mo>=</mo><mn>1</mn></math>;<span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span>b) <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mfrac><mn>1</mn><mn>5</mn></mfrac></mfenced><mi>x</mi></msup><mo> </mo><mo>=</mo><mo> </mo><mn>25</mn></math>;</p>
<p>c) <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>2</mn><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>2</mn></mrow></msup><mo> </mo><mo>=</mo><mo> </mo><mn>4</mn></math>;<span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span><span class="mce-nbsp-wrap" contenteditable="false"> </span>d) <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>0</mn><mo>,</mo><mn>5</mn></mrow></mfenced><mrow><mi>x</mi><mo>+</mo><mn>7</mn></mrow></msup><mo>.</mo><msup><mfenced><mrow><mn>0</mn><mo>,</mo><mn>5</mn></mrow></mfenced><mrow><mn>1</mn><mo>-</mo><mn>2</mn><mi>x</mi></mrow></msup><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn></math></p>
<p><strong><em>Hướng dẫn giải:</em></strong></p>
<p>a) <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>0</mn><mo>,</mo><mn>3</mn></mrow></mfenced><mrow><mn>3</mn><mi>x</mi><mo>-</mo><mn>2</mn></mrow></msup><mo>=</mo><mn>1</mn><mo>⇔</mo><msup><mfenced><mrow><mn>0</mn><mo>,</mo><mn>3</mn></mrow></mfenced><mrow><mn>3</mn><mi>x</mi><mo>-</mo><mn>2</mn></mrow></msup><mo>=</mo><msup><mfenced><mrow><mn>0</mn><mo>,</mo><mn>3</mn></mrow></mfenced><mn>0</mn></msup><mo>⇔</mo><mn>3</mn><mi>x</mi><mo>-</mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo>⇔</mo><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math></p>
<p>Vậy <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mfenced open="{" close="}"><mfrac><mn>2</mn><mn>3</mn></mfrac></mfenced></math>.</p>
<p>b) <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mfrac><mn>1</mn><mn>5</mn></mfrac></mfenced><mi>x</mi></msup><mo> </mo><mo>=</mo><mo> </mo><mn>25</mn><mo> </mo><mo>⇔</mo><mo> </mo><msup><mn>5</mn><mrow><mo>-</mo><mi>x</mi></mrow></msup><mo> </mo><mo>=</mo><mo> </mo><msup><mn>5</mn><mn>2</mn></msup><mo> </mo><mo>⇔</mo><mo> </mo><mi>x</mi><mo>=</mo><mo>-</mo><mn>2</mn></math>. Vậy S = {-2}.</p>
<p>c) <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>2</mn><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>2</mn></mrow></msup><mo> </mo><mo>=</mo><mo> </mo><mn>4</mn><mo>⇔</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn><mo>⇔</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo>⇔</mo><msubsup><mo>[</mo><mrow><mi>x</mi><mo>=</mo><mn>3</mn></mrow><mrow><mi>x</mi><mo>=</mo><mn>0</mn></mrow></msubsup></math></p>
<p>Vậy S = {0;3}</p>
<p>d) <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>0</mn><mo>,</mo><mn>5</mn></mrow></mfenced><mrow><mi>x</mi><mo>+</mo><mn>7</mn></mrow></msup><mo>.</mo><msup><mfenced><mrow><mn>0</mn><mo>,</mo><mn>5</mn></mrow></mfenced><mrow><mn>1</mn><mo>-</mo><mn>2</mn><mi>x</mi></mrow></msup><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn><mo>⇔</mo><msup><mfenced><mrow><mn>0</mn><mo>,</mo><mn>5</mn></mrow></mfenced><mrow><mn>8</mn><mo>-</mo><mi>x</mi></mrow></msup><mo> </mo><mo>=</mo><mo> </mo><msup><mfenced><mrow><mn>0</mn><mo>,</mo><mn>5</mn></mrow></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>⇔</mo><mn>8</mn><mo>-</mo><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mn>1</mn><mo>⇔</mo><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mn>9</mn></math></p>
<p>Vậy S = {9}.</p>
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