Answer
$x\approx6.06$
Work Step by Step
Find the natural log of both sides and then pull out the exponent to the left side. Then solve for $x$.
$5^{x-3}=137$
$\ln(5^{x-3})=\ln(137)$
$(x-3)\ln(5)=\ln(137)$
$(x-3)=\frac{\ln(137)}{\ln(5)}$
$x=3+\frac{\ln(137)}{\ln(5)}$
$x\approx6.06$
