1. Solve the equation $3^{x^{2}+x-2}-3^{x^{2}-4}=80$.
6.II.1. Let's rewrite the equation as $3^{x^{2}-4}\left(3^{x+2}-1\right)=80$ and set $f(x)=3^{x^{2}-4}\left(3^{x+2}-1\right)$. If $x \leqslant -2$, then $f(x) \leqslant 0$, hence the equation has no solutions on the interval $(-\infty; -2]$. If $-2 < x \leqslant 0$, then $0 < 3^{x+2} - 1 \leqslant 8$ and $3^{x^{2}-4} \leqslant 1$, so $f(x) \leqslant 1$, hence the equation has no solutions on the interval $(-2; 0]$. Now notice that the function $f(x)$ is increasing on the interval $[0; +\infty)$, so the equation has at most one solution. It remains to note that $f(2)=80$, so $x=2$ is a solution to the equation. Answer: $\{2\}$.