# Math Help - Finding the Inverse of a Logarithmic Function

1. ## Finding the Inverse of a Logarithmic Function

Hey Guys, I am looking to send in my homework by tomorrow morning and was hoping someone would help me with this question.

What is the equation of the inverse function of the following:

y = -log(base 5) (-x)

y = -log(base 5) (-x)
Why is this harder than the other 100 you have done successfully?

1) Think it through.

Domain x < 0. Do you see why?

2) Swap and Solve

$x = -log_{5}(-y)$

$-x = log_{5}(-y)$

$5^{-x} = -y$

$-\left(5^{-x}\right) = y$

3) Well, that's the algebra. Does it work? Is it a function? Does it need restrictions? Why did I worry about the original Domain?

3. I'm always nervous when I post four questions and get no response. I DO hope you get it.

4. Oops, I thought I replied you but I must have forgotten.

Yes I did get it, your help is verrry much appreciated