Question

Solve the following equation:
$\log \left(\log x\right)+\log (\log x^4-3)=0$

Answer 1

$log\left(logx\right)+log(log{x}^4-3)=0\Rightarrow log\left(logx\right)+log(4logx-3)=0\Rightarrow logx(4logx-3)=1\Rightarrow 4{\left(logx\right)}^2-3logx-1=0\Rightarrow logx=1,logx=\frac{-1}{4}\Rightarrow x=10,\frac{1}{\sqrt[4]{410}}.$