Answer
$x=9.386$
Work Step by Step
The given expression can be written as:
$ e^{3x-7-2x}=4e $
This implies that $ e^{x-7} =4e$
We need to take natural log of both sides and apply logarithmic property : $\log a^ b=b \log a$ .
$(x-7) \ln e=\ln 4e$
Now, we will evaluate the result for $x$.
$x-7 =2.386$
Therefore, our answer is: $x=9.386$