Hướng dẫn Giải Bài 2 (Trang 68, SGK Toán Giải Tích 12)

Hướng dẫn giải Bài 2 (Trang 68 SGK Toán Giải Tích 12)

Bài 2 (Trang 68 SGK Toán Giải Tích 12): Tính: a) <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>4</mn><mrow><msub><mi>log</mi><mn>2</mn></msub><mfenced><mn>3</mn></mfenced></mrow></msup></math>; b) <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>27</mn><mrow><msub><mi>log</mi><mn>9</mn></msub><mfenced><mn>2</mn></mfenced></mrow></msup></math>; c) <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>9</mn><mrow><msub><mi>log</mi><msqrt><mn>3</mn></msqrt></msub><mfenced><mn>2</mn></mfenced></mrow></msup></math>; d) <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>4</mn><mrow><msub><mi>log</mi><mn>8</mn></msub><mfenced><mn>27</mn></mfenced></mrow></msup></math>. Hướng dẫn giải: Áp dụng <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>a</mi><mrow><msub><mi>log</mi><mi>a</mi></msub><mfenced><mi>b</mi></mfenced></mrow></msup><mo>=</mo><mi>b</mi></math> a) <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>4</mn><mrow><msub><mi>log</mi><mn>2</mn></msub><mfenced><mn>3</mn></mfenced></mrow></msup><mo>=</mo><msup><mn>2</mn><mrow><mn>2</mn><msub><mi>log</mi><mn>2</mn></msub><mfenced><mn>3</mn></mfenced></mrow></msup><mo>=</mo><msup><mn>2</mn><mrow><msub><mi>log</mi><mn>2</mn></msub><mfenced><msup><mn>3</mn><mn>2</mn></msup></mfenced></mrow></msup><mo>=</mo><mn>9</mn></math> b) <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>27</mn><mrow><msub><mi>log</mi><mn>9</mn></msub><mfenced><mn>2</mn></mfenced></mrow></msup><mo>=</mo><msup><mn>3</mn><mrow><mn>3</mn><msub><mi>log</mi><msup><mn>3</mn><mn>2</mn></msup></msub><mfenced><mn>2</mn></mfenced></mrow></msup><mo>=</mo><msup><mn>3</mn><mrow><msub><mi>log</mi><mn>3</mn></msub><mfenced><msup><mn>2</mn><mfrac><mn>3</mn><mn>2</mn></mfrac></msup></mfenced></mrow></msup><mo>=</mo><msup><mn>2</mn><mfrac><mn>3</mn><mn>2</mn></mfrac></msup><mo>=</mo><mn>2</mn><msqrt><mn>2</mn></msqrt></math>; c) <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>9</mn><mrow><msub><mi>log</mi><msqrt><mn>3</mn></msqrt></msub><mfenced><mn>2</mn></mfenced></mrow></msup><mo>=</mo><msup><mn>3</mn><mrow><mn>2</mn><msub><mi>log</mi><msup><mn>3</mn><mfrac><mn>1</mn><mn>2</mn></mfrac></msup></msub><mfenced><mn>2</mn></mfenced></mrow></msup><mo>=</mo><msup><mn>3</mn><mrow><mn>4</mn><msub><mi>log</mi><mn>3</mn></msub><mfenced><mn>2</mn></mfenced></mrow></msup><mo>=</mo><msup><mn>3</mn><mrow><msub><mi>log</mi><mn>3</mn></msub><mfenced><msup><mn>2</mn><mn>4</mn></msup></mfenced></mrow></msup><mo>=</mo><msup><mn>2</mn><mn>4</mn></msup><mo>=</mo><mn>16</mn></math>; d) <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>4</mn><mrow><msub><mi>log</mi><mn>8</mn></msub><mfenced><mn>27</mn></mfenced></mrow></msup><mo>=</mo><msup><mn>2</mn><mrow><mn>2</mn><msub><mi>log</mi><msup><mn>2</mn><mn>3</mn></msup></msub><mfenced><msup><mn>3</mn><mn>3</mn></msup></mfenced></mrow></msup><mo>=</mo><msup><mn>2</mn><mrow><msub><mi>log</mi><mn>2</mn></msub><mfenced><msup><mn>3</mn><mn>2</mn></msup></mfenced></mrow></msup><mo>=</mo><msup><mn>3</mn><mn>2</mn></msup><mo>=</mo><mn>9</mn></math>