Hướng dẫn giải Bài 1 (Trang 68 SGK Toán Giải Tích 12)

Bài 1 (Trang 68 SGK Toán Giải Tích 12): Không sử dụng máy tính, hãy tính: a) <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>2</mn></msub><mfenced><mfrac><mn>1</mn><mn>8</mn></mfrac></mfenced></math>; b) <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mfrac><mn>1</mn><mn>4</mn></mfrac></msub><mfenced><mn>2</mn></mfenced></math>; c) <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>3</mn></msub><mfenced><mroot><mn>3</mn><mn>4</mn></mroot></mfenced></math>; d) <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mrow><mn>0</mn><mo>,</mo><mn>5</mn></mrow></msub><mfenced><mrow><mn>0</mn><mo>,</mo><mn>125</mn></mrow></mfenced></math>. Hướng dẫn giải: Áp dụng: <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><msup><mi>a</mi><mi>α</mi></msup></msub><mfenced><msup><mi>a</mi><mi>β</mi></msup></mfenced><mo>=</mo><mfrac><mi>β</mi><mi>α</mi></mfrac></math> a) <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>2</mn></msub><mfenced><mfrac><mn>1</mn><mn>8</mn></mfrac></mfenced><mo>=</mo><msub><mi>log</mi><mn>2</mn></msub><mfenced><msup><mn>2</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mfenced><mo>=</mo><mo>-</mo><mn>3</mn></math> b) <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mfrac><mn>1</mn><mn>4</mn></mfrac></msub><mfenced><mn>2</mn></mfenced><mo>=</mo><msub><mi>log</mi><msup><mn>2</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup></msub><mfenced><mn>2</mn></mfenced><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math> c) <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>3</mn></msub><mfenced><mroot><mn>3</mn><mn>4</mn></mroot></mfenced><mo>=</mo><msub><mi>log</mi><mn>3</mn></msub><mfenced><msup><mn>3</mn><mfrac><mn>1</mn><mn>4</mn></mfrac></msup></mfenced><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac></math> d) <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mrow><mn>0</mn><mo>,</mo><mn>5</mn></mrow></msub><mfenced><mrow><mn>0</mn><mo>,</mo><mn>125</mn></mrow></mfenced><mo>=</mo><msub><mi>log</mi><mrow><mn>0</mn><mo>,</mo><mn>5</mn></mrow></msub><msup><mfenced><mrow><mn>0</mn><mo>,</mo><mn>5</mn></mrow></mfenced><mn>3</mn></msup><mo>=</mo><mn>3</mn></math>