# Formula of an inverse function

1. Sep 9, 2014

### wertlewoo2

1. The problem statement, all variables and given/known data
Find the formula of the inverse function of f(x)=300/(3+15e^.05x).

2. Relevant equations

f(x)=300/(3+15e^.05x)

3. The attempt at a solution

I'm definitely way off but I got .05y(5x)+ln100=lnx. What I did was multiple the denominator by the y(cross mltiplication) and then tried to factor out e.

2. Sep 9, 2014

### Staff: Mentor

Welcome to PF!

So you start with y = 300 / (3 + 15 e^(x/20)

and do the cross product trick to get y * (3 + 15e^(x/20)) = 300

and then to:

3 + 15e^(x/20) = 300 / y

Does this help?

You should now move terms and factors to the y side and you should then be able to isolate everything
so that you get x = ...

3. Sep 9, 2014

### wertlewoo2

@Jedishrfu Thanks so much that was really helpful!! Last question do you know how you could be able to take the ln of e to simplify the equation?

4. Sep 9, 2014

### Staff: Mentor

I'm sure he does. The real question is do you know how? If you do, take a stab at it.

If you don't, review the properties of logarithms.

5. Sep 9, 2014

### Staff: Mentor

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