Решите неравенство:

$log _{\frac{1}{3}} (x^{2} -4)\ \textless \ log _{\frac{1}{3}} (-3x)$

ОДЗ:
$\left \{ {{x^2-4\ \textgreater \ 0} \atop {-3x\ \textgreater \ 0}} \right. ~~~~~ \left \{ {{(x+2)(x-2)\ \textgreater \ 0} \atop {x\ \textless \ 0}} \right.$

//////////// $-2$ __________ $2$ ____-> x

//////////////////////// $0$ __________-> x

$x\in (-\infty;-2)$

Решение:
$log _{\frac{1}{3}} (x^{2} -4)\ \textless \ log _{\frac{1}{3}} (-3x) \\ x^2-4\ \textgreater \ -3x \\ x^2+3x-4\ \textgreater \ 0 \\ (x+4)(x-1)\ \textgreater \ 0 \\ \\ ///////////////////\\----(\text{-4)}----\text{(-2)}-----(1)----\ \textgreater \ x \\ ////////~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~/////////$

Ответ: $x\in (-\infty;-4)$