310. Вычислить: 1) \(\frac{\log_8 8}{\log_8 16}\); 2) \(\frac{\log_5 27}{\log_5 9}\); 3) \(\frac{\log_5 36-\log_5 12}{\log_5 9}\); 4) \(\frac{\log_7 8}{\log_7 15-\log_7 30}\).

1. \(\frac{1}{\log_8 16}=\frac{1}{4/3}=\frac34\).
2. \(\frac{\log_5 27}{\log_5 9}=\log_9 27=\frac32\).
3. \(\frac{\log_5(36/12)}{\log_5 9}=\frac{\log_5 3}{\log_5 9}=\frac12\).
4. \(\frac{\log_7 8}{\log_7(15/30)}=\frac{\log_7 8}{\log_7(1/2)}=-3\), поскольку \((\frac12)^{-3}=8\).

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