Answer
$x\approx0.55$
Work Step by Step
Begin by factoring the terms using trial and error. Then set the terms in each set of parentheses equal to $0$ and solve for $x$ by using the natural log on both sides of each equation.
$e^{4x}+5e^{2x}-24=0$
$(e^{2x}+8)(e^{2x}-3)=0$
$(e^{2x}+8)=0, (e^{2x}-3)=0$
$e^{2x}=-8, e^{2x}=3$
not possible, $2x=\ln(3)$
$x=\frac{\ln(3)}{2}$
$x\approx0.55$
