Question

Solve the following equation:
$\log \left(\log x\right)+\log (\log x^3-2)=0$

Answer 1

$log\left(logx\right)+log(log{x}^3-2)=0$

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

$\Rightarrow log[lo{g}_{x}log{x}^3-2logx]=0$

$\Rightarrow log[3lo{g}^{2}x-2logx]=0$

$\Rightarrow 3lo{g}^{2}x-2logx=1$

$\Rightarrow 3lo{g}^{2}x-3logx+logx-1=0$

$\Rightarrow 3logx(logx-1)+1(logx-1)=0$

$logx=1$ or $logx=-1/3$

$x=10$ or $x={10}^{-1/3}$