Answer
$x=7$
Work Step by Step
Given"
$27^{x+1}=9^{x+5}$
Since $27=3^{3} \text{ and } 9=3^{2}$, then the equation above is equivalent to:
$\left(3^{3}\right)^{x+1}=\left(3^{2}\right)^{x+5}$
Using the rule $\left(a^{m}\right)^{n}=a^{m n}$, the equation above simplifies to
$3^{3(x+1)}=3^{2(x+5)}$
When bases are equal then exponents must be equal so
$3(x+1)=2(x+5)$
$3x+3=2 x+10$
$3x-2x=10-3$
$x=7$
