## College Algebra (6th Edition)

$x=5$
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. $x=5$