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Help with inverse function

  1. Nov 23, 2009 #1

    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. jcsd
  3. Nov 23, 2009 #2
    Is the function f(x) = log (x/3) or f(x) = (log x)/3 ? First, solve for the independent variable:

    [tex]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[/tex]

    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
  4. Nov 23, 2009 #3
    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
  5. Nov 24, 2009 #4


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    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.
  6. Nov 24, 2009 #5
    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?
  7. Nov 25, 2009 #6
    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.
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