Решите неравенство<3

Решите задачу:

$log_2(x-3)log_2(x-3)\ \textless \ 3\; ,\; \; ODZ:\; \; x\ \textgreater \ 3\\\\log^2_2(x-3)-3\ \textless \ 0\\\\(log_2(x-3)-\sqrt3)(log_2(x-3)+\sqrt3)\ \textless \ 0\\\\t=log_2(x-3)\; ,\; \; (t-\sqrt3)(t+\sqrt3)\ \textless \ 0\; \to \; \; -\sqrt3\ \textless \ t\ \textless \ \sqrt3\\\\ \left \{ {{log_2(x-3)\ \textgreater \ -\sqrt3} \atop {log_2(x-3)\ \textless \ \sqrt3}} \right. \; \left \{ {{x-3\ \textgreater \ 2^{-\sqrt3}} \atop {x-3\ \textless \ 2^\sqrt3}} \right. \; \left \{ {{x\ \textgreater \ 3+2^{-\sqrt3}} \atop {x\ \textless \ 3+2^{\sqrt3}}} \right. \\\\Otvet:\; \; x\in (3+2^{-\sqrt3};3+2^{\sqrt3}).$