Решите неравенство: [latex] log _{\frac{1}{3}} (x^{2} -4)\ \textless \ log _{\frac{1}{3}} (-3x)[/latex]

[latex] log _{\frac{1}{3}} (x^{2} -4)\ \textless \ log _{\frac{1}{3}} (-3x)[/latex] ОДЗ: [latex] \left \{ {{x^2-4\ \textgreater \ 0} \atop {-3x\ \textgreater \ 0}} \right. ~~~~~ \left \{ {{(x+2)(x-2)\ \textgreater \ 0} \atop {x\ \textless \ 0}} \right. [/latex] ////////////[latex]-2[/latex]__________[latex]2[/latex]____->   x ////////////////////////[latex]0[/latex]__________->  x [latex]x\in (-\infty;-2)[/latex] Решение: [latex]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 \\ ////////~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~/////////[/latex] Ответ: [latex]x\in (-\infty;-4)[/latex]