Решите неравенство: log(осн. 7) (х-1) + log(осн. 7) (х-7) < 1

Решите задачу:

$log_7(x-1)+log_7(x-7)\ \textless \ 1\; ;\; \; \; ODZ:\; \left \{ {{x-1\ \textgreater \ 0} \atop {x-7\ \textgreater \ 0}} \right. \; \to \; x\ \textgreater \ 7\\\\log_7((x-1)(x-7))\ \textless \ log_77\\\\x^2-8x+7\ \textless \ 7\\\\x^2-8x\ \textless \ 0\\\\x(x-8)\ \textless \ 0\; \; \; \; \; \; \; +++(0)---(8)+++\\\\x\in (0,8)\\\\ \left \{ {{x\in (0,8)} \atop {x\ \textgreater \ 7}} \right. \; \; \Rightarrow \; \; \; x\in (7,8)\\\\==$