Question

Solve the following equation:
$|x-1{|}^{{\log }^{2}x-\log x^3}=|x-1{|}^3$

Answer 1

$\log \left(\log x\right)+\log \left[\log \right(x^{3)}-2]=0\Rightarrow \log [\log x(3\log x-2)]=0\Rightarrow 3({\log x)}^2-2\log x=1\Rightarrow 3{\left(\log x\right)}^2-2\log x-1=0$

Therefore, $\log x=1,\frac{-1}{3}$

Therefore, $x=10,{10}^{\frac{-1}{3}}$