Question

log1/3(x^2 +8x)=-2
Помогите решить!

Answer 1

ОДЗ
$x^{2} +8x textgreater 0 \ \ x(x+8) textgreater 0$

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__________-8_________0______________

x∈(-∞; -8)∪(0; +∞)

$log_{ frac{1}{3}} (x^2 +8x)=-2 \ \ x^{2} +8x=( frac{1}{3})^{-2} \ \ x^{2} +8x=9 \ \ x^{2} +8x-9=0 \ \ x^{2} -x+9x-9=0 \ \ x(x-1)+9(x-1)=0 \ \ (x+9)(x-1)=0 \ \ x_1=-9 \ \ x_2=1$

Ответ 9; -1