3. Вычислите: logs log2 16

Решение:

$$log_8 log_2 16$$

$$log_8 log_2 16 = log_8 log_2 2^4 = log_8 (4log_2 2) = log_8 (4 \cdot 1) = log_8 4 = log_8 8^{\frac{2}{3}} = \frac{2}{3}log_8 8 = \frac{2}{3} \cdot 1 = \frac{2}{3}$$

Ответ: $$\frac{2}{3}$$