[tex]\displaystyle\\
3^{2x}-2\cdot 3^x-3=10\\
(3^x)^2-2\cdot 3^x-3-10=0 \\
(3^x)^2-2\cdot 3^x-7=0 \\
\text{Notam: }t=3^x\\
t^2-2t-7=0\\\\
t_{12}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\\\\
\frac{2\pm\sqrt{4+28}}{2}=\frac{2\pm \sqrt{32}}{2}=\frac{2\pm 4\sqrt{2}}{2}=1\pm 2\sqrt{2}\\\\
t_1=1+2\sqrt{2}~\Longrightarrow~ 3^x=1+2\sqrt{2}~\Longrightarrow~ \boxed{x=\log_3(1+2\sqrt{2})}\\ \\
t_2=1-2\sqrt{2}~\Longrightarrow~ 3^x=1-2\sqrt{2}~\Longrightarrow~ \boxed{x=\log_3(1-2\sqrt{2})}
[/tex]
