3. Найдите корень уравнения log2(x + 6) = log2(6x – 11) – 2.

Решим уравнение:

$$log_2(x + 6) = log_2(6x - 11) - 2$$

$$log_2(x + 6) = log_2(6x - 11) - log_2(2^2)$$

$$log_2(x + 6) = log_2(6x - 11) - log_2(4)$$

$$log_2(x + 6) = log_2(\frac{6x - 11}{4})$$

$$x + 6 = \frac{6x - 11}{4}$$

$$4(x + 6) = 6x - 11$$

$$4x + 24 = 6x - 11$$

$$2x = 35$$

$$x = 17.5$$

Ответ: 17.5