# How do you find the inverse of #y=log_(1/2) x#?

##### 2 Answers

Jan 9, 2016

It's

by logic you put

You find the identity application so

Jan 9, 2016

#### Explanation:

Given

By the nature of what a log is, another way of writing the given relationship is:

As it turns out this is exactly the format needed for the inverse function. All you have to now do is swap the variable letters round to give:

So if

Then

Or, if you prefer