# How do you find the inverse of y= log_6 (x+2)?

Oct 13, 2016

$x = {6}^{y} - 2$

#### Explanation:

$\textcolor{w h i t e}{\text{XXX}} c = {\log}_{b} a \Leftrightarrow a = {b}^{c}$

Therefore
$\textcolor{w h i t e}{\text{XXX}} y = {\log}_{6} \left(x + 2\right) \Leftrightarrow {6}^{y} = x + 2$

From which it follows that
$\textcolor{w h i t e}{\text{XXX}} {6}^{y} - 2 = x$