Question

2×log8(2x)+log8(x-1)^2=4/3

Answer 1

ОДЗ: $\left \{ {{2x\ \textgreater \ 0} \atop {x-1\ \textgreater \ 0}} \right. \to \left \{ {{x\ \textgreater \ 0} \atop {x\ \textgreater \ 1}} \right. \to x\ \textgreater \ 1$

$\log_8(((2x)^2(x-1)^2)=\log_88^{ \frac{4}{3} } \\ (2x)^2(x-1)^2=16\\ x^2(x-1)^2=4$


x(x-1)=2
x²-x-2=0
x1=-1
x2=2

Ответ: 2.