# Inverse of a logarithmic function

## Homework Statement

Greetings everyone! I am having problems getting started with this question, which asks:

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

## 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.

Try using this :

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

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.

Mark44
Mentor
Try using this :

$log(y) = log \left(\frac{3-4e^x}{6-10e^x}\right)$
I don't see that this is a helpful hint.

Mark44
Mentor

## Homework Statement

Greetings everyone! I am having problems getting started with this question, which asks:

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

## 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.
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.

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