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Math Help - relationship between power and log transformation

  1. #1
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    relationship between power and log transformation

    Not sure if this is the correct forum, but I was wondering if a log transformation can be expressed in terms of a power transformation. That is, can you take the implicit function x^y=log(x) and make it explicit by solving for y?

    I mean I can solve for y easily but the result isn't satisfactory because it still includes the "log(x)" function, so you'd have an infinitely nested part of the equation if you keep substituting log(x) with x^y.
    Last edited by danjohnson10; April 19th 2011 at 04:58 PM.
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  2. #2
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    Assume the base is 10.
    x^y = log x
    log x^y = log log x
    y log x = log log x
    ∴ y = (log log x)/log x
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  3. #3
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    Yes, I can see that, but you still have log(x) in the equation. So if you were to express a log transformation strictly as a power transformation would it not be impossible? You would still have to take the log of x in order to do so which defeats the whole purpose of such a conversion. I guess I answered my own question. Sorry
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