Answer
$x=\frac{3}{2}$
Work Step by Step
We are given that $9^{x+1}=243$. Both of these numbers are powers of 3, so we can rewrite the equation as $(3^{2})^{x+1}=3^{2x+2}=3^{5}$.
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, $2x+2=5$. To solve for x, subtract 2 from both sides.
$2x=3$
Divide both sides by 2.
$x=\frac{3}{2}$
