Answer
$x=-\frac{1}{3}$
Work Step by Step
We are given that $27^{x+1}=9$. Both of these numbers are powers of 3, so we can rewrite the equation as $(3^{3})^{x+1}=3^{3x+3}=3^{2}$.
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, $3x+3=2$.
Subtract 3 from both sides.
$3x=-1$
Divide both sides by 3.
$x=-\frac{1}{3}$
