#### Answer

$x=-\dfrac{1}{3}$

#### Work Step by Step

$27^{x+1}=9$
Rewrite $27$ as $3^{3}$ and $9$ as $3^{2}$:
$(3^{3})^{x+1}=3^{2}$
Transform the left side of the equation into a power that has the product of $3$ and $x+1$ as its exponent:
$3^{3x+3}=3^{2}$
If $3^{3x+3}=3^{2}$, then $3x+3=2$
$3x+3=2$
Solve for $x$:
$3x=2-3$
$3x=-1$
$x=-\dfrac{1}{3}$