Answer
$x = log_{3}(\frac{11}{9})$
Work Step by Step
$$3^{x + 2} = 11$$
Converting the equation to logarithm:
$log_{3}(11) = x + 2$
$x = log_{3}(11) - 2$; if we consider the constant term $2$ as being multiplied by $1$, we can re-write this in the following manner:
$x = log_{3}(11) - 2[1]$
$= log_{3}(11) - 2[log_{3}(3)]$
$= log_{3}(11) - log_{3}(3)^{2}$
$= log_{3}(11) - log_{3}(9)$; and apply logarithmic rules to finally achieve:
$x = log_{3}(\frac{11}{9})$
