6. Найдите корень уравнения $$log_2(3x + 7) = log_2(10x + 16) - 1$$.

Решим уравнение:

$$log_2(3x + 7) = log_2(10x + 16) - 1$$ $$log_2(3x + 7) = log_2(10x + 16) - log_22$$ $$log_2(3x + 7) = log_2(\frac{10x + 16}{2})$$ $$3x + 7 = \frac{10x + 16}{2}$$ $$2(3x + 7) = 10x + 16$$ $$6x + 14 = 10x + 16$$ $$10x - 6x = 14 - 16$$ $$4x = -2$$ $$x = \frac{-2}{4}$$ $$x = -0.5$$

Ответ: x = -0.5