Question

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

Answer 1

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

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

$xin (-infty;-2)$

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: $xin (-infty;-4)$