Inverse of a logarithmic function

[togame]

Homework Statement

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

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

Homework Equations

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.

 

[rollcast]

Try using this :

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

 

[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.

 

[Mark44]

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]

Homework Statement

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

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

Homework Equations

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 e^x to the left side, and all the other terms to the right side. Finally, factor out e^x and isolate it.

 

[togame]

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