Answer
$x =-\dfrac{(\ln{13})-1}{2}$
Work Step by Step
Take the natural logarithm of both sides to obtain:
$\ln{e^{-2x+1}} = \ln{13}$
RECALL:
$\ln{e^a} = a$
Use the rule above to obtain:
$-2x+1=\ln{13}$
Subtract by $1$ on both sides of the equation to obtain:
$\begin{array}{ccc}
&-2x+1 -1 &= &\ln{13}-1
\\&-2x &= &\ln{13}-1
\end{array}$
Divide by $-2$ on both sides of the equation to obtain:
$x =\dfrac{\ln{13}-1}{-2}
\\x =-\dfrac{\ln{13}-1}{2}$