Question

Solve the following equations.
$x^{\log x+1}={10}^6$

Answer 1

$x^{logx+1}={10}^6\Rightarrow logx+1=6{log}_{x}10\Rightarrow logx+1=\frac{6}{logx}\Rightarrow {\left(logx\right)}^2+logx-6=0\Rightarrow (logx+3)(log-2)=0$

Therefore, $logx=-3$ or $2.$

Therefore, $x=\frac{1}{1000}$ or $100$

$x={10}^{-3}$ or ${10}^2.$