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

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