Answer
$x=\dfrac{\ln5}{6}\approx0.2682$
Work Step by Step
$e^{6x}=5$
Apply $\ln$ to both sides of the equation:
$\ln e^{6x}=\ln5$
Take $6x$ to multiply in front of its respective $\ln$:
$6x\ln e=\ln5$
Since $\ln e=1$, this equation simplifies to:
$6x=\ln5$
Solve for $x$:
$x=\dfrac{\ln5}{6}\approx0.2682$