Answer
$(-\infty,\infty)$
Work Step by Step
We have to solve the exponential equation:
$3^{3x+6}=27^{x+2}$
Rewriting $27$ as $3^{3}$, we have
$3^{3x+6}=(3^{3})^{x+2}$
$\implies 3^{3x+6}=3^{3x+6}$
Equating the exponents, we have
$3x+6=3x+6$
Since the above equation is true for infinite values of $x$, the equation has infinitely many solutions.
