Question

Solve the following equation:
$2{\log }_8\left(2x\right)+{\log }_8(x^2+1-2x)=\frac{4}{3}$

Answer 1

Consider Domain

$x>0$ and $x$ is not equal to $1$

$⟹2lo{g}_2\left(2x\right)+lo{g}_2(x^2-2x+1)=4$

By trial and Error Method

Put $x=2$

Equation is Satisfied..