Question

Solve for x :
$5^{\log x}+5x^{\log 5}=3\left(a>0\right);$ when the base of the log is a

Answer 1

$let{\log }_{a}x=z$

$5^z+5.5^z=3$

$let{5}^z=p$

$p\left(6\right)=3$

$p=\frac{1}{2}$

$5^z=\frac{1}{2}$

$z\log 5=-\log 2$

$z=-\frac{\log 2}{\log 5}$

${\log }_{a}x=-{\log }_{5}2$

$x=a^{-{\log }_{5}2}$