Решите неравенство. Справа ответ.

Решите задачу:

$log_2\; log_{\frac{1}{3}}\, log_5x\ \textgreater \ 0\; ,\\\\ODZ: \left\{\begin{array}{l}x\ \textgreater \ 0\\log_5x\ \textgreater \ 0\\log_{\frac{1}{3}}log_5x\ \textgreater \ 0}\end{array}\right \; \; \left\{\begin{array}{l}x\ \textgreater \ 0\\log_5x\ \textgreater \ log_51\\log_{\frac{1}{3}}(log_5x)\ \textgreater \ log_{\frac{1}{3}}1}\end{array}\right \; \left\{\begin{array}{l}x\ \textgreater \ 0\\x\ \textgreater \ 1\\log_5x\ \textless \ 1\end{array}\right\\\\\\\left\{\begin{array}{l}x\ \textgreater \ 0\\x\ \textgreater \ 1\\x\ \textless \ 5\end{array}\right\; \; \to \; \; \; 1\ \textless \ x\ \textless \ 5\\\\\\log_2(log_{\frac{1}{3}}(log_5x))\ \textgreater \ log_21\; \; \to \; \; \; log_{\frac{1}{3}}(log_5x)\ \textgreater \ 1\; \; \; \to$

$log_{\frac{1}{3}}(log_5x)\ \textgreater \ log_{\frac{1}{3}} \frac{1}{3} \; \; \; \to \; \; \; log_5x\ \textless \ \frac{1}{3}\; \; \; \to \\\\log_5x\ \textless \ log_5\, 5^{\frac{1}{3}}\; \; \; \to \; \; \; x\ \textless \ 5^{\frac{1}{3}}\; \; \; \; ili\; \; \; \; x\ \textless \ \sqrt[3]5\\\\ \left \{ {{1\ \textless \ x\ \textless \ 5} \atop {x\ \textless \ \sqrt[3]5}} \right. \; \; \; \to \; \; \; 1\ \textless \ x\ \textless \ \sqrt[3]5\\\\Otvet:\; \; x\in (1;\sqrt[3]5)\; .$