Answer
$x\approx11.48$
Work Step by Step
Find the natural log of both sides and then pull out the exponent to the left side. Then solve for $x$.
$7^{0.3x}=813$
$\ln(7^{0.3x})=\ln(813)$
$0.3x\ln(7)=\ln(813)$
$0.3x=\frac{\ln(813)}{\ln(7)}$
$x=\frac{\ln(813)}{\ln(7)}\times\frac{1}{0.3}$
$x\approx11.48$
