# What is the inverse of y=log(x-4)+2 ?

Mar 2, 2018

${10}^{x - 2} + 4$ is the inverse.

#### Explanation:

We have the function $f \left(x\right) = y = \log \left(x - 4\right) + 2$

To find ${f}^{-} 1 \left(x\right)$, we take our equation:

$y = \log \left(x - 4\right) + 2$

Switch the variables:

$x = \log \left(y - 4\right) + 2$

And solve for $y$:

$x - 2 = \log \left(y - 4\right)$

We can write $x - 2$ as $\log \left({10}^{x - 2}\right)$, so we have:

$\log \left({10}^{x - 2}\right) = \log \left(y - 4\right)$

As the bases are the same:

$y - 4 = {10}^{x - 2}$

$y = {10}^{x - 2} + 4$