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Math Help - help for my son

  1. #1
    Newbie
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    help for my son

    Can someone help me solve this for my son? I have gone blank!

    I need to solve this for Y.

    C.X^Y = P.Y

    thanks
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  2. #2
    MHF Contributor
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    Re: help for my son

    As far as I know, Y(X) cannot be expressed in elementary functions in general.
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  3. #3
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    Re: help for my son

    Mark.. Emakarov is right

    you cannot express y as an algebraic expression ...since it is trancedental.
    such type of equations can be solved only by approximation or graphically .
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  4. #4
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    Re: help for my son

    thanks guys. I thought I was losing it, but what you say makes sense.
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  5. #5
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    Re: help for my son

    X^y= e^{ln(X^Y)= e^{Y ln(X)} so the equation can be written as Ce^{Y ln(X)}= PY or \frac{C}{P}= Ye^{-Yln(X)}. Let Z= -Yln(X). Then Y= -Zln(X) and e^{-Yln(X)}= e^Z so the equation becomes \frac{C}{P}= -Zln(X)e^Z and then -\frac{C}{PZln(X)}= Ze^Z.

    Now apply "Lambert's W function" to both sides. "Lambert's W function" is defined as the inverse function to f(x)= xe^x so W(Ze^Z)= Z= W\left(-\frac{C}{PZln(X)}\right). Of course, "Lambert's W function" is NOT an "elementary function" so emakarov is completely correct.
    Last edited by HallsofIvy; June 14th 2013 at 07:24 AM.
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