# How do you find the inverse of y=log_2(x+4)?

Jan 11, 2016

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

#### Explanation:

For finding the inverse follow these steps.

Step 1: Swap $x$ and $y$
Step 2: Solve for $y$
Step 3: Write the result in the correct notation.

To find inverse of $y = {\log}_{2} \left(x + 4\right)$

Step 1: Swap $x$ and $y$

$x = {\log}_{2} \left(y + 4\right)$

Step 2: Solve for $y$

Convert the log to exponent form.
$\mathmr{if} {\log}_{b} \left(a\right) = k$ then $a = {b}^{k}$

We have $x = {\log}_{2} \left(y + 2\right)$
${2}^{x} = y + 2$

Subtracting $2$ on both the sides.
${2}^{x} - 2 = y$

$y = {2}^{x} - 2$ Inverse function

Step 3:

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