Помогите решить [latex]lg (x-1)^{6} =(x-5)lg|x-1|[/latex]

[latex]Formyla:\; \; \; log_{a}\, x^{2k}=2k\cdot log_{a}|x|\; ,\; \; 2k-chetnoe\; chislo\\\\lg(x-1)^6=(x-5)lg|x-1|\\\\6\cdot lg|x-1|-(x-5)\cdot lg|x-1|=0\\\\lg|x-1|\cdot (6-x+5)=0\\\\lg|x-1|\cdot (11-x)=0\\\\a)\; \; 11-x=0\; \; \to \; \; x=11\\\\b)\; \; lg|x-1|=0\; \; \to \; \; |x-1|=1\; \; \to \left [ {{x-1=1} \atop {x-1=-1}} \right. \; \left [ {{x=2} \atop {x=0}} \right. \\[/latex]