Log0,1(x-2)-lgx больше log0,1 3;

[latex]log_{0,1}(x-2)-lgx\ \textgreater \ log_{0,1} 3[/latex] ОДЗ: [latex] \left \{ {{x\ \textgreater \ 0} \atop {x-2\ \textgreater \ 0}} \right. [/latex] [latex] \left \{ {{x\ \textgreater \ 0} \atop {x\ \textgreater \ 2}} \right. [/latex] --------------(0)------------------                    /////////////////// -------------------(2)-------------                            //////////// [latex]x[/latex] ∈ [latex](2;+[/latex] ∞ [latex])[/latex] [latex]log_{10^{-1}}(x-2)-lgx\ \textgreater \ log_{10^{-1}} 3[/latex] [latex]-lg(x-2)-lgx\ \textgreater \ -lg 3[/latex] [latex]lg(x-2)+lgx\ \textless \ \ lg 3[/latex] [latex]lg[x(x-2)]\ \textless \ \ lg 3[/latex] [latex]lg(x^2-2x)\ \textless \ \ lg 3[/latex] [latex]x^2-2x\ \textless \ \ 3[/latex] [latex]x^2-2x-3\ \textless \ 0[/latex] [latex]D=(-2)^2-4*1*(-3)=4+12=16[/latex] [latex]x_1= \frac{2+4}{2} =3[/latex] [latex]x_1= \frac{2-4}{2} =-1[/latex] -----+----(-1)---- - ----(3)------+------                  ////////////// -------------------(2)--------------------                           //////////////////// Ответ: (2; 3)