Answer
$x= \dfrac{\ln 5}{6}$
Work Step by Step
Taking the natural logarithm of both sides, the given equation, $
e^{6x}=5
,$ is equivalent to
\begin{array}{l}\require{cancel}
\ln e^{6x}= \ln 5
.\end{array}
Using the properties of logarithms and that $\ln e=1$, the solution to the equation above is
\begin{array}{l}\require{cancel}
6x\ln e= \ln 5
\\\\
6x(1)= \ln 5
\\\\
6x= \ln 5
\\\\
x= \dfrac{\ln 5}{6}
.\end{array}
