[latex]log_6(2x^2-7x+6)-log_6(x-2)=log_6x[/latex]

[latex]log_6(2x^2-7x+6)-log_6(x-2)=log_6x[/latex] ОДЗ: [latex] \left \{ {{2x^2-7x+6\ \textgreater \ 0} \atop {x-2\ \textgreater \ 0}}\atop {x\ \textgreater \ 0}} \right. [/latex] [latex] \left \{ {{2(x-2)(x-1.5)\ \textgreater \ 0} \atop {x\ \textgreater \ 2}}\atop {x\ \textgreater \ 0}} \right. [/latex] [latex]2x^2-7x+6=0[/latex] [latex]D=(-7)^2-4*2*6=1[/latex] [latex]x_1= \frac{7+1}{4}=2 [/latex] [latex]x_2= \frac{7-1}{4}=1.5[/latex] -------+------(1.5)------ - --------(2)-----+--------- ////////////////                            ////////////////                                                /////////////// ----------(0)------------------------(2)---------------                ////////////////////////////////////////////// [latex]x[/latex] ∈ [latex](2; +[/latex] ∞ [latex])[/latex] [latex]log_6(2x^2-7x+6)=log_6x+log_6(x-2)[/latex] [latex]log_6(2x^2-7x+6)=log_6[x(x-2)][/latex] [latex]log_6(2x^2-7x+6)=log_6(x^2-2x)[/latex] [latex]2x^2-7x+6=x^2-2x[/latex] [latex]2x^2-7x+6-x^2+2x=0[/latex] [latex]x^2-5x+6=0[/latex] [latex]D=(-5)^2-4*1*6=1[/latex] [latex]x_1= \frac{5+1}{2} =3[/latex] [latex]x_2= \frac{5-1}{2} =2[/latex] ∅ Ответ: 3