Answer
0.833
Work Step by Step
We are given the equation $9^{-x+2}=13$. In order to solve, we must first take the natural log of both sides.
$ln(9^{-x+2})=ln(13)$
$(-x+2)ln(9)=ln(13)$
Divide both sides by $ln(9)$.
$-x+2=\frac{ln(13)}{ln(9)}$
Subtract 2 from both sides.
$-x=\frac{ln(13)}{ln(9)}-2$
Multiply both sides by -1.
$x=-\frac{ln(13)}{ln(9)}+2\approx0.833$
