Formula of an inverse function

[wertlewoo2]

Homework Statement

Find the formula of the inverse function of f(x)=300/(3+15e^.05x).

Homework Equations

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

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.

 

[jedishrfu]

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 = ...

 

[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?

 

[Mark44]

@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?

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.

 

[jedishrfu]

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.