Question

Solve the following equation:
$x^{\frac{\log x+7}{4}}={10}^{\log x+1}$

Answer 1

$x\frac{logx+7}{4}={10}^{logx+1}\Rightarrow \frac{logx+7}{4}=(logx+1)\left({log}_{x}10\right)\Rightarrow \frac{logx+7}{4}=\frac{logx+1}{logx}\Rightarrow {\left(logx\right)}^2+7logx=4logx+4\Rightarrow (logx{)}^2+3logx-4=0\Rightarrow (logx+4)(logx-1)=0$

$\Rightarrow logx=-4$ or $1$

$\Rightarrow x={10}^{-4}$ or $10.$