5. Решите уравнение log₈ x + log√₂ x = 14.

5. Решите уравнение $$log_8 x + log_{\sqrt{2}} x = 14$$.

$$log_8 x + log_{\sqrt{2}} x = 14$$

$$log_{2^3} x + log_{2^{\frac{1}{2}}} x = 14$$

$$\frac{1}{3}log_2 x + 2log_2 x = 14$$

$$\frac{7}{3}log_2 x = 14$$

$$log_2 x = 14 \times \frac{3}{7}$$

$$log_2 x = 6$$

$$x = 2^6$$

$$x = 64$$

Ответ: 64