Answer
$x=\dfrac{e^5}{2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\ln(2x)=5
,$ convert it to exponential form. Then 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(2x)=5
.\end{array}
Since $y=b^x$ is equivalent to $\log_b y=x,$ the exponential form of the equation above is
\begin{array}{l}\require{cancel}
e^5=2x
.\end{array}
Using the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
2x=e^5
\\\\
x=\dfrac{e^5}{2}
.\end{array}
