Answer
$x=\frac{4}{3}$
Work Step by Step
We are given the exponential equation $125^{x}=625$.
We can express each side using a common base and then solve for $x$.
$125^{x}=(5^{3})^{x}=5^{3x}$
$625=5^{4}$
$5^{3x}=5^{4}$
Take the natural log of both sides.
$ln(5^{3x})=ln(5^{4})$
$3xln(5)=4ln(5)$
Divide both sides by $ln(5)$.
$3x=4$
Divide both sides by 3.
$x=\frac{4}{3}$
