Log1/3(x-1) больше 2, 1/3 в основании

[latex]log_{ \frac{1}{3} }(x-1)\ \textgreater \ 2 [/latex] ОДЗ: [latex]x-1\ \textgreater \ 0[/latex] [latex]x\ \textgreater \ 1[/latex] [latex]log_{ \frac{1}{3} }(x-1)\ \textgreater \ log_{ \frac{1}{3} } \frac{1}{9} [/latex] [latex](x-1)\ \textless \ \frac{1}{9} [/latex] [latex]x\ \textless \ 1\frac{1}{9} [/latex] С учетом ОДЗ Ответ:[latex](1; 1\frac{1}{9} )[/latex]