x\in\{2,3,4,5,6,8,9,10,11,12\}" alt="\frac{1}{2}\log_{x-1}(x^2-26x+169)+\log_{13-x}(14x-x^2-13)\ \textgreater \ 3\\\\
\frac{1}{2}\log_{x-1}(13-x)^2+\log_{13-x}((x-1)(13-x))\ \textgreater \ 3\\\\
\log_{x-1}(13-x)+\log_{13-x}(x-1)+\log_{13-x}(13-x)\ \textgreater \ 3\\\\
\log_{x-1}(13-x)+\frac{1}{\log_{x-1}(13-x)}\ \textgreater \ 2\\\\
y = \log_{x-1}(13-x)\\\\
y+\frac{1}{y}\ \textgreater \ 2 =\ \textgreater \ y\ \textgreater \ 0; y\neq 1\\\\
0\ \textless \ \log_{x-1}(13-x)\neq1\\\\
\left\{\begin{matrix}
x-1\ \textgreater \ 0\\
13-x\ \textgreater \ 0\\
x-1\neq 13-x
\end{matrix}\right\\\\ x\in Z => x\in\{2,3,4,5,6,8,9,10,11,12\}" align="absmiddle" class="latex-formula">
Всего 10 целочисленных решений