Hướng dẫn Giải Bài 4 (Trang 68, SGK Toán Giải Tích 12)

Hướng dẫn giải Bài 4 (Trang 68 SGK Toán Giải Tích 12)

Bài 4 (Trang 68 SGK Toán Giải Tích 12): So sánh các cặp số sau: a) <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>3</mn></msub><mfenced><mn>5</mn></mfenced></math> và <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>7</mn></msub><mfenced><mn>4</mn></mfenced></math>; b) <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mrow><mn>0</mn><mo>,</mo><mn>3</mn></mrow></msub><mfenced><mn>2</mn></mfenced></math> và <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>5</mn></msub><mfenced><mn>3</mn></mfenced></math>; c) <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>2</mn></msub><mfenced><mn>10</mn></mfenced></math> và <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>5</mn></msub><mfenced><mn>30</mn></mfenced></math>. Hướng dẫn giải: a) <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>3</mn></msub><mfenced><mn>5</mn></mfenced><mo>></mo><msub><mi>log</mi><mn>3</mn></msub><mfenced><mn>3</mn></mfenced><mo>=</mo><mn>1</mn><mo>;</mo><msub><mi>log</mi><mn>7</mn></msub><mfenced><mn>4</mn></mfenced><mo><</mo><msub><mi>log</mi><mn>7</mn></msub><mfenced><mn>7</mn></mfenced><mo>=</mo><mn>1</mn></math> Vậy <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>3</mn></msub><mfenced><mn>5</mn></mfenced><mo>></mo><msub><mi>log</mi><mn>7</mn></msub><mfenced><mn>4</mn></mfenced></math> b) <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mrow><mn>0</mn><mo>,</mo><mn>3</mn></mrow></msub><mfenced><mn>2</mn></mfenced><mo><</mo><msub><mi>log</mi><mrow><mn>0</mn><mo>,</mo><mn>3</mn></mrow></msub><mfenced><mn>1</mn></mfenced><mo>=</mo><mn>0</mn><mo>;</mo><mo> </mo><msub><mi>log</mi><mn>5</mn></msub><mfenced><mn>3</mn></mfenced><mo>></mo><msub><mi>log</mi><mn>5</mn></msub><mfenced><mn>1</mn></mfenced><mo>=</mo><mn>0</mn></math> Vậy <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mrow><mn>0</mn><mo>,</mo><mn>3</mn></mrow></msub><mfenced><mn>2</mn></mfenced><mo><</mo><msub><mi>log</mi><mn>5</mn></msub><mfenced><mn>3</mn></mfenced></math> c) <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>2</mn></msub><mfenced><mn>10</mn></mfenced><mo>></mo><msub><mi>log</mi><mn>2</mn></msub><mfenced><mn>8</mn></mfenced><mo>=</mo><msub><mi>log</mi><mn>2</mn></msub><mfenced><msup><mn>2</mn><mn>3</mn></msup></mfenced><mo>=</mo><mn>3</mn><mo>;</mo><mo> </mo><msub><mi>log</mi><mn>5</mn></msub><mfenced><mn>30</mn></mfenced><mo><</mo><msub><mi>log</mi><mn>5</mn></msub><mfenced><mn>125</mn></mfenced><mo>=</mo><msub><mi>log</mi><mn>5</mn></msub><mfenced><msup><mn>5</mn><mn>3</mn></msup></mfenced><mo>=</mo><mn>3</mn></math> Vậy <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>2</mn></msub><mfenced><mn>10</mn></mfenced><mo>></mo><msub><mi>log</mi><mn>5</mn></msub><mfenced><mn>30</mn></mfenced></math>.