2. Решите уравнения: б) log(1/4) (x² + 6x) = - 2;

б) log_{$$\frac{1}{4}$$(x² + 6x) = -2}

x² + 6x = ($$\frac{1}{4}$$)^-2

x² + 6x = 4²

x² + 6x = 16

x² + 6x - 16 = 0

D = 36 + 64 = 100

x₁ = $$\frac{-6 + 10}{2}$$ = 2

x₂ = $$\frac{-6 - 10}{2}$$ = -8

Проверка:

x = 2: log_{$$\frac{1}{4}$$(4 + 12) = log$$\frac{1}{4}$$16 = -2}

x = -8: log_{$$\frac{1}{4}$$(64 - 48) = log$$\frac{1}{4}$$16 = -2}

Ответ: -8; 2