# How do you find the inverse function f(x) = 18 + ln(x)?

Oct 22, 2015

If memory serves me correctly: $\text{ } y = {e}^{x - 18}$
I would recommend you check this against another source!

#### Explanation:

Given that $f \left(x\right) = \ln \left(x\right) + 18$

Write as $y = \ln \left(x\right) + 18$

Then $\ln \left(x\right) = y - 18$

Consider another way of writing $\ln \left(x\right)$

This is in fact ${e}^{\text{something}} = x$

In this case $\text{something} = y - 18$ giving:

$x = {e}^{y - 18}$

Now all you have to do is exchange the letters $\text{ "x " and } y$ giving:

$y = {e}^{x - 18}$