Неравенство log(1/3)2*log(5)(x-2)>0

Решите задачу:

$log_{\frac{1}{3}}2\cdot log_5(x-2)\ \textgreater \ 0\; ,\; \; \; \; ODZ:\; \; x-2\ \textgreater \ 0\; ,\; \; x\ \textgreater \ 2\\\\log_{\frac{1}{3}}2\ \textless \ 0\; \; \; \Rightarrow \; \; \; log_5(x-2)\ \textless \ 0\\\\log_5(x-2)\ \textless \ log_51\\\\x-5\ \textless \ 1\\\\x\ \textless \ 6\\\\Otvet:\; \; \; x\in (2,6)\; .$