Answer
$x\approx 1.213$
Work Step by Step
$e^{3x-1}=14\qquad \color{blue}{\text{ ...apply ln(...) to both sides } }$
$\ln(e^{3x-1})=\ln 14\qquad \color{blue}{\text{ ...apply } \log_{a}a^{x}=x}$
$3x-1=\ln 14$
$3x=1+\ln 14$
$x=\displaystyle \frac{1+\ln 14}{3}$
$x\approx 1.213$
