Question

Solve the following equation:
$x^{\frac{\log x+5}{3}}={10}^{5+\log x}$

Answer 1

$x\frac{logx+5}{3}={10}^{5+logx}\Rightarrow \left(\frac{logx+5}{3}\right)logx=5+logx\Rightarrow ({logx)}^2+5logx=15+3logx\Rightarrow ({logx)}^2+2logx-15=0\Rightarrow (logx+5)(logx-3)=0$

Therefore, $logx=-5$ or $3$

Therefore, $x={10}^{-5}$ or ${10}^3.$