Решите пожалуйста [latex]lo g _{x-1}(2 x^{2} - 5 x - 3) = 2 [/latex]

ОДЗ: [latex]x-1\ \textgreater \ 0;x\ \textgreater \ 1[/latex] [latex]x-1 \neq 1;x \neq 2[/latex] [latex]2x^2-5x-3\ \textgreater \ 0;(x-3)(2x+1)\ \textgreater \ 0; \left \{ {{x\ \textgreater \ 3} \atop {x\ \textless \ - \frac{1}{2} }} \right. [/latex] (3;+∞) [latex]log _{x-1}(2 x^{2} - 5 x - 3) = 2 [/latex] [latex]lo g _{x-1}(2 x^{2} - 5 x - 3) = log_{x-1}(x-1)^2[/latex] [latex]2x^2-5x-3=(x-1)^2[/latex] [latex]2x^2-5x-3=x^2-2x+1[/latex] [latex]x^2-3x-4=0[/latex] [latex](x-4)(x+1)=0[/latex] [latex]x_1=4;x_2=-1[/latex] Ответ с учетом ОДЗ: 4