smc

Let $2^x=a$. Because $2^{2x}=(2^x{)}^2$, the given expression can be rewritten as $a^2-8a+12=0$. This can be factored as $(a-6)(a-2)=0$, which has solutions $a=2^x=6$ and $a=2^x=2$. Looking at the answer choices, we see that $x=1$ is absent. Rewriting $2^x=6$ as $x=lo{g}_{2}6$ and then applying the logarithm addition identity in reverse gives $x=lo{g}_2(2)+lo{g}_2(3)=1+lo{g}_2(3)$. Applying the logarithm division identity shows that the answer is $\boxed{1+\frac{log(3)}{log(2)}}$.