Question

Find the value of $x$ which satisfies the equation: $3^{{\log }_5(x-7)}={\log }_5\left(125\right)$

Answer 1

$3^{{\log }_5(x-7)}$ is valid when $x>7$

$3^{{\log }_5(x-7)}={\log }_5\left(5^3\right)$

$3^{{\log }_5(x-7)}=3{\log }_5\left(5\right)$

$3^{{\log }_5(x-7)}=3^1$

Equating the power of 3

$\Rightarrow {\log }_5(x-7)=1$

$\Rightarrow x-7=5$

$\Rightarrow x=12$
Ans: 12