Решите неравенство: [latex]log _{ \frac{2}{ \sqrt{5} } } \frac{5x}{5x-1} \ \textless \ 0[/latex]

[latex] 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}. \\ [/latex] ОДЗ: [latex] \frac{5x}{5x-1}\ \textgreater \ 0; \\ 5x(5x-1)\ \textgreater \ 0; \\ [/latex] x∈(-∞;0)∪(1/5;+∞). Ответ: (1/5;+∞).