Решите пожалуйста [latex]lo g _{7}(3-x)+lo g _{7}(4-10x)=2lo g _{7} 6[/latex]

[latex]lo g _{7}(3-x)+lo g _{7}(4-10x)=2lo g _{7} 6[/latex] ОДЗ: [latex] \left \{ {{3-x\ \textgreater \ 0} \atop {4-10x\ \textgreater \ 0}} \right. [/latex] [latex] \left \{ {{-x\ \textgreater \ -3} \atop {-10x\ \textgreater \ -4}} \right. [/latex] [latex] \left \{ {{x\ \textless \ 3} \atop {x\ \textless \ 0.4}} \right. [/latex] [latex]x[/latex] ∈ [latex](-[/latex] ∞ [latex];0.4)[/latex] [latex]lo g _{7}[(3-x)(4-10x)]=lo g _{7} 6^2[/latex] [latex]lo g _{7}(10x^2-34x+12)=lo g _{7} 36[/latex] [latex]10x^2-34x+12= 36[/latex] [latex]10x^2-34x+12- 36=0[/latex] [latex]10x^2-34x- 24=0[/latex] [latex]5x^2-17x- 12=0[/latex] [latex]D=(-17)^2-4*5*(-12)=289+240=529[/latex] [latex]x_1= \frac{17+23}{10}=4 [/latex] - ∅ [latex]x_2= \frac{17-23}{10}=-0.6[/latex] Ответ: -0,6