6) log27-log2; 7 16 496. a) lg 8+1g 18 21g2+lg 3, B) log2 11-log2 44; r) log0,3 9-2 logo.3 10.

б) Вычислим $$log_2 7 - log_2 \frac{7}{16}$$:

$$log_2 7 - log_2 \frac{7}{16} = log_2 \frac{7}{\frac{7}{16}} = log_2 (7 \cdot \frac{16}{7}) = log_2 16 = log_2 2^4 = 4$$

Ответ: 4

496. a) Вычислим $$\frac{lg 8 + lg 18}{2lg 2 + lg 3}$$:

$$\frac{lg 8 + lg 18}{2lg 2 + lg 3} = \frac{lg (8 \cdot 18)}{lg 2^2 + lg 3} = \frac{lg 144}{lg 4 + lg 3} = \frac{lg 144}{lg (4 \cdot 3)} = \frac{lg 144}{lg 12} = \frac{lg 12^2}{lg 12} = \frac{2 lg 12}{lg 12} = 2$$

Ответ: 2

B) Вычислим log₂ 11 - log₂ 44:

$$log_2 11 - log_2 44 = log_2 \frac{11}{44} = log_2 \frac{1}{4} = log_2 2^{-2} = -2$$

Ответ: -2

г) Вычислим log_0.3 9 - 2 log_0.3 10:

$$log_{0.3} 9 - 2 log_{0.3} 10 = log_{0.3} 9 - log_{0.3} 10^2 = log_{0.3} 9 - log_{0.3} 100 = log_{0.3} \frac{9}{100} = log_{0.3} (\frac{3}{10})^2 = 2 log_{0.3} \frac{3}{10} = 2 log_{0.3} 0.3 = 2 \cdot 1 = 2$$

Ответ: 2