Answer
$x=5$
Work Step by Step
We are given the exponential equation $5^{2-x}=\frac{1}{125}$.
We can express each side using a common base and then solve for $x$.
$5^{2-x}=5^{-3}=\frac{1}{5^{3}}\frac{1}{125}$
Take the natural log of both sides.
$ln(5^{2-x})=ln(5^{-3})$
$(2-x)ln(5)=-3ln(5)$
Divide both sides by $ln(5)$.
$2-x=-3$
Subtract 2 from both sides.
$-x=-5$
Divide both sides by -1.
$x=5$
