7) log1(7 -2x) + log1 = log115; 2 1 8 1 2

7) $$log_{\frac{1}{2}}(7 - 2x) + log_{\frac{1}{2}} \frac{1}{8} = log_{\frac{1}{2}}15$$

Используем свойство логарифмов: log_a b + log_a c = log_a (b*c)

$$log_{\frac{1}{2}}((7 - 2x) \cdot \frac{1}{8}) = log_{\frac{1}{2}}15$$

$$\frac{7 - 2x}{8} = 15$$

$$7 - 2x = 120$$

$$-2x = 113$$

$$x = -\frac{113}{2} = -56.5$$

Проверка:

$$log_{\frac{1}{2}}(7 - 2 \cdot (-56.5)) + log_{\frac{1}{2}} \frac{1}{8} = log_{\frac{1}{2}}15$$

$$log_{\frac{1}{2}}(7 + 113) + log_{\frac{1}{2}} \frac{1}{8} = log_{\frac{1}{2}}15$$

$$log_{\frac{1}{2}}(120) + log_{\frac{1}{2}} \frac{1}{8} = log_{\frac{1}{2}}15$$

$$log_{\frac{1}{2}}(120 \cdot \frac{1}{8}) = log_{\frac{1}{2}}15$$

$$log_{\frac{1}{2}}15 = log_{\frac{1}{2}}15$$

Ответ: $$x = -56.5$$