Hướng dẫn Giải Bài 6 (Trang 90, SGK Toán Giải Tích 12)

Hướng dẫn giải Bài 6 (Trang 90 SGK Toán Giải Tích 12)

Bài 6 (Trang 90 SGK Toán Giải Tích 12): Cho logab = 3, logac = -2. Hãy tính logax với: a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mo> </mo><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup><msqrt><mi mathvariant="normal">c</mi></msqrt></math>; b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><msup><mi mathvariant="normal">a</mi><mn>4</mn></msup><mroot><mi mathvariant="normal">b</mi><mn>3</mn></mroot></mrow><msup><mi mathvariant="normal">c</mi><mn>3</mn></msup></mfrac></math>. Hướng dẫn giải: Áp dụng tính chất logarit của tích và thương, ta có; <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><msub><mi>log</mi><mi>a</mi></msub><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><msub><mi>log</mi><mi>a</mi></msub><msup><mi>a</mi><mn>3</mn></msup><mo> </mo><mo>+</mo><mo> </mo><msub><mi>log</mi><mi>a</mi></msub><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msub><mi>log</mi><mi>a</mi></msub><msqrt><mi>c</mi></msqrt><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn><mo>+</mo><mn>2</mn><msub><mi>log</mi><mi>a</mi></msub><mi>b</mi><mo> </mo><mo>+</mo><mo> </mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msub><mi>log</mi><mi>a</mi></msub><mi>c</mi><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn><mo>+</mo><mn>2</mn><mo>.</mo><mn>3</mn><mo> </mo><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>(</mo><mo>-</mo><mn>2</mn><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mn>8</mn></math>.  <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>)</mo><mo> </mo><msub><mi>log</mi><mi>a</mi></msub><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><msub><mi>log</mi><mi>a</mi></msub><msup><mi>a</mi><mn>4</mn></msup><mroot><mi>b</mi><mn>3</mn></mroot><mo>-</mo><msub><mi>log</mi><mi>a</mi></msub><msup><mi>c</mi><mn>3</mn></msup><mo> </mo><mo>=</mo><mo> </mo><msub><mi>log</mi><mi>a</mi></msub><msup><mi>a</mi><mn>4</mn></msup><mo>+</mo><msub><mi>log</mi><mi>a</mi></msub><mroot><mi>b</mi><mn>3</mn></mroot><mo>-</mo><msub><mi>log</mi><mi>a</mi></msub><msup><mi>c</mi><mn>3</mn></msup><mo> </mo><mspace linebreak="newline"/><mo>=</mo><mo> </mo><mn>4</mn><mo>+</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msub><mi>log</mi><mi>a</mi></msub><mi>b</mi><mo>-</mo><mn>3</mn><msub><mi>log</mi><mi>a</mi></msub><mi>c</mi><mo> </mo><mo>=</mo><mo> </mo><mn>4</mn><mo>+</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>.</mo><mn>3</mn><mo>-</mo><mn>3</mn><mo>(</mo><mo>-</mo><mn>2</mn><mo>)</mo><mo> </mo><mspace linebreak="newline"/><mo>=</mo><mo> </mo><mn>11</mn></math>.