Answer
$x=\frac{1}{2}$
Work Step by Step
We are given that $9^{2x+1}=81$. Both of these numbers are powers of 9, so we can rewrite the equation as $9^{2x+1}=9^{2}$.
From the uniqueness of $b^{x}$, we know that $b^{x}=b^{y}$ is equivalent to $x=y$ (when $b\gt0$ and $b\ne1$).
Therefore, $2x+1=2$.
Subtract 1 from both sides..
$2x=1$
Divide both sides by 2.
$x=\frac{1}{2}$