Answer
$x=1$
Work Step by Step
Letting $u=3^x$, the given equation becomes:
$u^2-u-6=0$
Factor the trinomial to obtain:
$(u-3)(u+2)=0$
Equate each factor to zero then solve each equation to obtain:
$\begin{array}{ccc}
&u-3=0 &\text{ or } &u+2=0
\\&u=3 &\text{ or } &u=-2
\end{array}$
Replace $u$ with $3^x$ to obtain:
$3^x=3 \text{ or } 3^x=-2
\\3^x=3^1 \text{ or } 3^x=-2$
Use the rule $a^m=a^n\longrightarrow m=n$ to solve the first equation and have:
$x=1$
The second equation has no solution since there is no real number that will make $3^x=-2$.
Thus, the only solution is $x=1$.