# Homework Help: Inverse of a logarithmic function

1. Jan 5, 2012

### togame

1. The problem statement, all variables and given/known data
Greetings everyone! I am having problems getting started with this question, which asks:

Find the inverse of $y = \frac{3-4e^x}{6-10e^x}$

2. Relevant equations

3. The attempt at a solution

I'm usually pretty good with these kinds of problems, but for some reason I seem to be unable to completely grasp this one. I can get one step and I'm not even sure that it's right.
$$y(6-10e^x) = 3-4e^x$$

After that I'm stuck. I can't seem to isolate e. Either I'm misunderstanding the law of logarithms or I just don't know. If someone could point me in the right direction, it would be greatly appreciated.

2. Jan 5, 2012

### rollcast

Try using this :

$log(y) = log \left(\frac{3-4e^x}{6-10e^x}\right)$

3. Jan 5, 2012

### togame

So my next step would be to simplify the right side using log laws, yes?
$$log(y)=log(3-4e^x)-log(6-10e^x)$$

This seems wrong but it's the only way I know.

4. Jan 5, 2012

### Staff: Mentor

I don't see that this is a helpful hint.

5. Jan 5, 2012

### Staff: Mentor

Multiply out the left side, and then move all the terms with ex to the left side, and all the other terms to the right side. Finally, factor out ex and isolate it.

6. Jan 5, 2012

### togame

Ah I see it now. Don't know how I missed that before. Thanks for the help mark!