Answer
$x=-2$
Work Step by Step
We are given the exponential equation $e^{x+1}=\frac{1}{e}$.
We can express each side using a common base and then solve for $x$.
$e^{x+1}=e^{-1}=\frac{1}{e}$
Take the natural log of both sides.
$ln(e^{x+1})=ln(e^{-1})$
$(x+1)ln(e)=-ln(e)$
Divide both sides by $ln(e)$.
$x+1=-1$
Subtract 1 from both sides.
$x=-2$
