Question

Solve the following equation:
$\frac{1-2(\log x^2{)}^2}{\log x-2(\log x{)}^2}=1$

Answer 1

$\frac{1+2({logx}^2{)}^2}{logx-2(logx{)}^2}=1\Rightarrow 1-8(logx{)}^2=logx-2({logx)}^2\Rightarrow 6({logx)}^2+logx-1=0\Rightarrow logx=\frac{-1}{2},\frac{1}{3}\Rightarrow x={10}^{\frac{-1}{2}},{10}^{\frac{1}{3}}\Rightarrow x=\frac{1}{\sqrt{10}},\sqrt[3]{310}.$