Answer
$x = \dfrac{-4}{3}$
Work Step by Step
RECALL:
(i) If $a^M=a^N$, then $M=N.$
(ii) $\dfrac{1}{a^m} = a^{-m}.$
Use rule (ii) above to obtain
$e^{x+4} = e^{-2x}.$
Use rule (i) to obtain
$x+4 = -2x.$
Solve the equation:
$x+4+2x=-2x+2x
\\3x+4=0
\\3x+4-4=0-4
\\3x=-4
\\x = \dfrac{-4}{3}.$
