Question

Решите неравенство: $log _{ frac{2}{ sqrt{5} } } frac{5x}{5x-1} textless 0$

Answer 1

$log_{ frac{2}{ sqrt{5} } } frac{5x}{5x-1} textless 0; \ log_{ frac{2}{ sqrt{5} } } frac{5x}{5x-1} textless log_{ frac{2}{ sqrt{5} } }1; \ frac{5x}{5x-1} textgreater 1; \ frac{5x-5x+1}{5x-1} textgreater 0; \ frac{1}{5x-1} textgreater 0; \ 5x-1 textgreater 0; \ 5x textgreater 1; \ x textgreater frac{1}{5}.$
ОДЗ:
$frac{5x}{5x-1} textgreater 0; \ 5x(5x-1) textgreater 0;$
x∈(-∞;0)∪(1/5;+∞).
Ответ: (1/5;+∞).