ShirokovP

Verified answer

Log 1/4 (x^2 + 6x) = - 2

ОДЗ
x ∈ ( - ∞; - 6) ∪( 0; + ∞)

x^2 + 6x = (1/4)^(-2)
x^2 + 6x = (2^(-2))^(-2)
x^2 + 6x = (2^2)^2
x^2 + 6x = 4^2
x^2 + 6x = 16
x^2 + 6x - 16 =  0
D = 100
x1 = ( - 6 + 10)/2 = 2 ∈ ОДЗ
x2 = ( - 6 - 10)/2 = - 8 ∈ ОДЗ

Ответ
- 8; 2