#### Answer

$x=6$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\ln e^x-2\ln e=\ln e^4
,$ use the properties of logarithms to combine the logarithmic expressions. Then use the properties of equality to solve for the variable. Finally, do checking of the solution/s with the original equation.
$\bf{\text{Solution Details:}}$
Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the equation above is equivalent
\begin{array}{l}\require{cancel}
x\ln e-2\ln e=4\ln e
.\end{array}
Since $\ln e=1,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
x(1)-2(1)=4(1)
\\\\
x-2=4
\\\\
x=4+2
\\\\
x=6
.\end{array}
Upon checking, $
x=6
$ satisfies the original equation.