7. Решить уравнение log √3 x + log9 x = 10.

$$log_{\sqrt{3}} x + log_9 x = 10$$

$$log_{3^{\frac{1}{2}}} x + log_{3^2} x = 10$$

$$\frac{1}{\frac{1}{2}} log_3 x + \frac{1}{2} log_3 x = 10$$

$$2 log_3 x + \frac{1}{2} log_3 x = 10$$

$$\frac{5}{2} log_3 x = 10$$

$$log_3 x = 4$$

$$x = 3^4 = 81$$

Ответ: 81