Solving for the Inverse of log (x)/3

[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.

 

[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) = 3b^x. Through a similar process, if you have f(x) = (log x)/3, the inverse would be f^-1(x) = b^3x, I think.

 

[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

 

[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.

 

[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?

 

[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.