2. Решите уравнения: в) log 2 8/x - log 2 √2x = -0,5.

в) log₂$$\frac{8}{x}$$ - log₂$$\sqrt{2x}$$ = -0,5

log₂$$\frac{8}{x \cdot \sqrt{2x}}$$ = -0,5

$$\frac{8}{x \cdot \sqrt{2x}}$$ = 2^-0,5 = $$\frac{1}{\sqrt{2}}$$

x$$\sqrt{2x}$$ = 8$$\sqrt{2}$$

x² \cdot 2x = 64 \cdot 2

2x³ = 128

x³ = 64

x = 4

Проверка:

log₂$$\frac{8}{4}$$ - log₂$$\sqrt{2 \cdot 4}$$ = log₂2 - log₂$$\sqrt{8}$$ = 1 - log₂2$$\sqrt{2}$$ = 1 - (1 + $$\frac{1}{2}$$) = -$$\frac{1}{2}$$ = -0,5

Ответ: 4