#### Answer

$x\approx5.521$

#### Work Step by Step

In exponential form, the given logarithmic equation, $
\ln (4x-2)=3
,$ is equivalent to
\begin{array}{l}\require{cancel}
\log_e (4x-2)=3
\\\\
4x-2=e^3
.\end{array}
Hence, the value of the variable that satisfies the given equation is
\begin{array}{l}\require{cancel}
4x=e^3+2
\\\\
x=\dfrac{e^3+2}{4}
\\\\
x\approx5.521
.\end{array}