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

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Answer 1 · 2018-03-02T11:18:31

$10^(x-2)+4$ is the inverse.

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

To find $f^-1(x)$ , we take our equation:

$y=log(x-4)+2$

Switch the variables:

$x=log(y-4)+2$

And solve for $y$ :

$x-2=log(y-4)$

We can write $x-2$ as $log(10^(x-2))$ , so we have:

$log(10^(x-2))=log(y-4)$

As the bases are the same:

$y-4=10^(x-2)$

$y=10^(x-2)+4$

Which is your inverse.

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