Solving for the Inverse of log (x)/3

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Discussion Overview

The discussion centers around finding the inverse of the function log(x)/3, with participants exploring different interpretations of the function and its implications in the context of biostatistics, particularly in relation to logistic regression.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether the function is f(x) = log(x/3) or f(x) = (log x)/3, leading to different approaches for finding the inverse.
  • Another participant suggests that if f(x) = log(x)/3, the inverse function could be expressed as f-1(x) = b3x, though this is contingent on the base of the logarithm.
  • A later reply clarifies that the notation f-1{log(x)/c} likely refers to the inverse of a different function f, rather than the inverse of log(x)/c itself.
  • There is a mention of the logistic regression equation, raising the question of whether an inverse can be computed for it, indicating a potential connection to the original function.
  • One participant speculates that the way the equation is presented may be intended to simplify the discussion of inverses, despite the complexity of deriving a formula.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct interpretation of the function or the feasibility of finding its inverse. Multiple competing views remain regarding the nature of the function and its application in logistic regression.

Contextual Notes

There are unresolved assumptions regarding the base of the logarithm and the specific context in which the function is applied, particularly in relation to logistic regression.

smkm
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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.
 
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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:
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
 
[tex]f^{-1}(\frac{log(x)}{c})[/tex]

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.
 
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?
 
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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