Question

$x^{\frac{\log x+7}{4}}={10}^{\log x+1}$.

Answer 1

$X^{\frac{\log x+7}{4}}={10}^{\log x+1}$

$\frac{\log x+7}{4}={\log }_x{10}^{(\log x+1)}$

$\frac{\log x+7}{4}=\frac{(\log x+1)}{\log x}$

Let $\log x=t$

$\frac{t+7}{4}=\frac{t+1}{t}$

$t^2+7t=4t+4$

$t^2+3t-4=0$

$t^2+4t-t-4=0$

$t(t+4)-1(t+4)=0$

$t=1,-4$

$\log x=1,\log x=-4$

$x={10}^1,{10}^{-4}$