Answer
$\{\log_{2}3\}$ or $\{1.585\}$
Work Step by Step
... Substitute $t=2^{x}$
... the equation becomes
$t^{2}+t-12=0 \quad $... factors of -12 whose sum is +1...
$(t+4)(t-3)=0$
t is either -4 or 3.
$t=2^{x}=-4$ cannot be a solution as $2^{x}$ is never negative.
$t=2^{x}=3$
... Apply $\log_{2}$
$\log_{2}2^{x}=\log_{2}3$
$x=\log_{2}3\approx 1.585$
The solution set is $\{\log_{2}3\}$ or $\{1.585\}$
