294. Вычислить: 1) (log₃ 8)/(log₃ 16); 2) (log₅ 27)/(log₅ 9); 3) (log₅ 36 − log₅ 12)/(log₅ 9); 4) (log₇ 8)/(log₇ 15 − log₇ 30).

1. \(\frac{\log_3 8}{\log_3 16}=\frac{\log_3 2^3}{\log_3 2^4}=\frac34.\)
2. \(\frac{\log_5 27}{\log_5 9}=\frac{\log_5 3^3}{\log_5 3^2}=\frac32.\)
3. \(\frac{\log_5 36-\log_5 12}{\log_5 9}=\frac{\log_5 3}{\log_5 3^2}=\frac12.\)
4. \(\frac{\log_7 8}{\log_7 15-\log_7 30}=\frac{\log_7 8}{\log_7(1/2)}=\frac{3\log_7 2}{-\log_7 2}=-3.\)

Ответ: 1) \(\frac34\); 2) \(\frac32\); 3) \(\frac12\); 4) −3.