# What is the inverse of y=3ln(x+2) ?

Jan 4, 2016

$y = {e}^{\frac{x}{3}} - 2$

#### Explanation:

Swap the $x$ and $y$ and solve for $y$.

$x = 3 \ln \left(y + 2\right)$

$\frac{x}{3} = \ln \left(y + 2\right)$

To undo the natural logarithm, exponentiate both sides with base $e$. This undoes the natural logarithm altogether.

${e}^{\frac{x}{3}} = y + 2$

$y = {e}^{\frac{x}{3}} - 2$