Log0,2X>log0,6X Pleasee pomogitee))

Решите задачу:

$log_{0,2}x\ \textgreater \ log_{0,6}x\; ,\; \; \; \; ODZ:\; x\ \textgreater \ 0\\\\ \frac{lgx}{lg0,2} \ \textgreater \ \frac{lgx}{lg0,6} \, |\cdot (lg0,2\cdot lg0,6)\\\\lg\, 0,2\ \textless \ 0\; ;\; lg\, 0,6\ \textless \ 0\; \; \to \; \; lg0,2\cdot lg0,6\ \textgreater \ 0\; \; \Rightarrow \\\\lg0,6\cdot lgx\ \textgreater \ lg0,2\cdot lgx\\\\lgx(lg0,6-lg0,2)\ \textgreater \ 0\\\\lgx\cdot lg\frac{0,6}{0,2}\ \textgreater \ 0\\\\lgx\cdot lg3\ \textgreater \ 0\\\\lg3\ \textgreater \ 0\; \; \Rightarrow \; \; lgx\ \textgreater \ 0\\\\x\ \textgreater \ 1\\\\x\in (1;+\infty )$