Answer
$x \approx 6.06$
Work Step by Step
RECALL:
$\ln{a^b} = b \cdot \ln{a}$
Take the natural logarithm of both sides to obtain:
$\ln{5^{x-3}}=\ln{137}$
Use the rule above to obtain:
$(x-3)\ln{5}=\ln{137}$
Divide $\ln{5}$ on both sides to obtain:
$x-3= \dfrac{\ln{137}}{\ln{5}}$
Add $3$ on both sides of the equation to obtain:
$x = 3 +\dfrac{\ln{137}}{\ln{5}}$
Use a scientific calculator to obtain:
$x=6.056956027
\\x \approx 6.06$
