من فرض میکنم $Loga=Lna$:
$a^{Loga}=12 \Rightarrow Log(a^{Loga})=Log12 \Rightarrow Loga.Loga=Log12 $
$\Rightarrow (Loga)^2=Log12,Log12>0 \Rightarrow \sqrt{(Loga)^2} = \sqrt{Log12} \Rightarrow |Loga|=\sqrt{Log12}$
$ \Rightarrow Loga=\sqrt{Log12} \vee Loga=-\sqrt{Log12} \Rightarrow a=e^{\sqrt{Log12}}=a_1 \vee a=e^{-\sqrt{Log12}}=a_2$
$a_1+a_2=e^{\sqrt{Log12}}e^{-\sqrt{Log12}}=e^{\sqrt{Log12}-\sqrt{Log12}}=e^0=1$
$ \Box $
