Answer
$x=\frac{4}{3}$
Work Step by Step
We are given the exponential equation $5^{3x-1}=125$.
We can express each side using a common base and then solve for $x$.
$5^{3x-1}=5^{3}=125$
Take the natural log of both sides.
$ln(5^{3x-1})=ln(5^{3})$
$(3x-1)ln(5)=3ln(5)$
Divide both sides by $ln(5)$.
$3x-1=3$
Add 1 to both sides.
$3x=4$
Divide both sides by 3.
$x=\frac{4}{3}$
