[latex]log x_{0.5} (x-1) \ \textgreater \ -2[/latex]

[latex] log_{0.5} (x-1)\ \textgreater \ -2[/latex] ОДЗ: [latex]x-1\ \textgreater \ 0[/latex]          [latex]x\ \textgreater \ 1[/latex] [latex] log_{ 2^{-1} } (x-1)\ \textgreater \ -2[/latex] [latex]- log_{ 2 } (x-1)\ \textgreater \ -2[/latex] [latex]log_{ 2 } (x-1)\ \textless \ 2[/latex] [latex]log_{ 2 } (x-1)\ \textless \ log_{2} 4[/latex] [latex]x-1\ \textless \ 4[/latex] [latex]x\ \textless \ 5[/latex] с учётом  ОДЗ получаем  Ответ: [latex](1;5)[/latex]