How do you find the inverse of f(x)=3^(x+2)?

Dec 4, 2015

${f}^{-} 1 \left(x\right) = {\log}_{3} x - 2$

Explanation:

$f \left(x\right) = {3}^{x + 2}$
$\implies y = {3}^{x + 2}$
$\implies x + 2 = {\log}_{3} y$

Add $- 2$ to both sides:
$x + 2 - 2 = {\log}_{3} y - 2$
$\implies x = {\log}_{3} y - 2$
$\implies {f}^{-} 1 \left(x\right) = {\log}_{3} x - 2$