Answer
$x=e^{\frac{13}{3}}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
3\ln x=13
,$ use the properties of equality to isolate the $\ln$ expression. Then use the definition of the natural logarithms and convert to exponential form. Finally, use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Using the properties of equality to isolate the $\ln$ expression results to
\begin{array}{l}\require{cancel}
\dfrac{3\ln x}{3}=\dfrac{13}{3}
\\\\
\ln x=\dfrac{13}{3}
.\end{array}
Since $\ln x=\log_e x,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
\log_e x=\dfrac{13}{3}
.\end{array}
Since $\log_by=x$ is equivalent to $y=b^x$, the equation above, in exponential form, is equivalent to
\begin{array}{l}\require{cancel}
x=e^{\frac{13}{3}}
.\end{array}