#### Answer

$x=\dfrac{e^{16}}{5}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\ln(5x)=16
,$ use the definition of natural logarithms and convert to exponential form. Finally, use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Since $\ln x=\log_e x,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
\log_e(5x)=16
.\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}
5x=e^{16}
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
x=\dfrac{e^{16}}{5}
.\end{array}