## Precalculus (10th Edition)

$x=-2.$
$9^{x+1}=(3^2)^{x+1}=3^{2(x+1)}=3^{2x+2}$, hence the equation becomes: $3^{x}=3^{2x+2}$. We know that if $a\ne1,-1$, then $a^k=a^l\longrightarrow k=l$. Hence: $2x+2=x\\(2x+2)-x=x-x\\x+2=0\\(x+2)-2=0-2\\x=-2.$