2×log8(2x)+log8(x-1)^2=4/3

ОДЗ: [latex] \left \{ {{2x\ \textgreater \ 0} \atop {x-1\ \textgreater \ 0}} \right. \to \left \{ {{x\ \textgreater \ 0} \atop {x\ \textgreater \ 1}} \right. \to x\ \textgreater \ 1[/latex] [latex]\log_8(((2x)^2(x-1)^2)=\log_88^{ \frac{4}{3} } \\ (2x)^2(x-1)^2=16\\ x^2(x-1)^2=4[/latex] x(x-1)=2 x²-x-2=0 x1=-1 x2=2 Ответ: 2.