Answer
$x=4$
Work Step by Step
$5^{x-1}=125$
Rewrite this equation as $5^{x}\cdot5^{-1}=125$
$5^{x}\cdot5^{-1}=125$
Take $5^{-1}$ to divide the right side of the equation:
$5^{x}=\dfrac{125}{5^{-1}}$
$5^{x}=125(5)$
$5^{x}=625$
Rewrite $625$ as $5^{4}$ and use the one-to-one property to solve this equation:
$5^{x}=5^{4}$
$x=4$
