Answer
$x \approx 11.48$
Work Step by Step
The base in the exponential equation is $7$, so take the natural logarithm on both sides to obtain
$\ln{(7^{0.3x})}=\ln{813}.$
Use the power rule $\ln{a^x}=x\ln{a}$ to bring down the exponent:
$(0.3x)\ln{7} = \ln{813}.$
Divide both sides by $\ln{7}$ to obtain
$0.3x = \dfrac{\ln{813}}{\ln{7}}.$
Divide both sides by $0.3$ to obtain
$x = \dfrac{\frac{\ln{813}}{\ln{7}}}{0.3}.$
Use a calculator and round-off the answer to two decimal places to obtain
$x \approx 11.48.$
