Answer
$x \approx 6.06$
Work Step by Step
The base in the exponential equation is $5$, so take the natural logarithm on both sides to obtain
$\ln{5^{x-3}}=\ln{137}.$
Use the power rule $\ln{a^x}=x\ln{a}$ to bring down the exponent:
$(x-3)\ln{5} = \ln{137}.$
Divide both sides by $\ln{5}$ to obtain
$x-3 = \dfrac{\ln{137}}{\ln{5}}.$
Add $3$ to both sides to obtain
$x = \dfrac{\ln{137}}{\ln{5}}+3.$
Use a calculator and round-off the answer to two decimal places to obtain
$x \approx 6.06.$
