Answer
Solution set = $\{ 1 \}$
Work Step by Step
$3^{x+2}\cdot 3^{x}=81\quad \left\{\begin{array}{ll}
\mathrm{L}\mathrm{H}\mathrm{S}: & a^{n}\cdot a^{m}=a^{n+m}\\
\mathrm{R}\mathrm{H}\mathrm{S}: & 125=5^{3}
\end{array}\right.$
$3^{(x+2)+x}=3^{4}$
$ 3^{2x+2}=3^{4}\qquad $ ... exponential functions are one to one.
$2x+2=4$
$2x=2$
$ x=1$
Solution set = $\{ 1 \}$
