# Help with inverse function

1. Nov 23, 2009

### smkm

Hi

How do I take the inverse of log (x)/3? If it is just log (x), it seems quite easy to do but I don't know what to do with the division by 3.

I saw this equation in a biostatistics article and I just can't understand how to solve it. It's been so long since I did inverse functions and I would really appreciate your help.

2. Nov 23, 2009

### pbandjay

Is the function f(x) = log (x/3) or f(x) = (log x)/3 ? First, solve for the independent variable:

$$f(x)=\log_b (x/3) \Rightarrow b^{f(x)}=b^{\log_b (x/3)} \Rightarrow b^{f(x)}=x/3 \Rightarrow 3b^{f(x)}=x$$

And to find the inverse function, switch the independent and dependent variables: f-1(x) = 3bx. Through a similar process, if you have f(x) = (log x)/3, the inverse would be f-1(x) = b3x, I think.

Last edited: Nov 23, 2009
3. Nov 23, 2009

### smkm

Hi pbandjay

Thanks so much for your help!!

I think f(x) is (log x)/3. It is a bit confusing the way they wrote it in the article.

they had it written out like this:

f-1 {log (x)/c} where c is some constant

4. Nov 24, 2009

### HallsofIvy

$$f^{-1}(\frac{log(x)}{c})$$

that appears to be asking for f-1 OF log(x)/c for some other function f, not for the inverse function of log(x)/c.

5. Nov 24, 2009

### smkm

Thanks HallsofIvy

if that's the case, they were referring to the logistic regression equation. Is it possible to take the inverse of the logistic regression equation?

6. Nov 25, 2009

### g_edgar

Perhaps they wrote it that way because talking about the inverse is easy, while computing a formula for it is complicated and not useful in the discussion.