Question

Solve for x :

(a) $5^{\log x}+5^{\log 5}=3\left(a>0\right);$ where base of log is a

Answer 1

$5^{\log x}+5^{\log 5}=3$

$a^{\log 5\log x}+a^{(\log 5{)}^2}=3$

$a^{\log 5}(a^{\log x}+a^{\log 5})=3$

$5^{\log a}(x^{\log a}+5^{\log a})=3$

$5(x+5)=3⟹x=-5+\frac{3}{5}=\frac{-22}{5}$