Answer
$x=-\frac{4}{3}$
Work Step by Step
We are given the exponential equation $e^{x+4}=\frac{1}{e^{2x}}$.
We can express each side using a common base and then solve for $x$.
$e^{x+4}=e^{-2x}=e^{-(2x)}=\frac{1}{e^{2x}}$
Take the natural log of both sides.
$ln(e^{x+4})=ln(e^{-2x})$
$(x+4)ln(e)=-2xln(e)$
Divide both sides by $ln(e)$.
$x+4=-2x$
Subtract $x$ from both sides.
$4=-3x$
Divide both sides by -3.
$x=-\frac{4}{3}$
