Answer
$x=0.347$
Work Step by Step
The given expression can be written as:
$ e^{1-3x+5x}=2e $
This implies that $ e^{1+2x} =2e$
We need to take natural log of both sides and apply logarithmic property : $\log a^ b=b \log a$ .
$2x \ln e=\ln 2$
Now, we will evaluate the result for $x$.
$2x =0.693$
Therefore, our answer is: $x=0.347$