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If y=x^x then what is x in terms of y?

  1. Jul 16, 2009 #1
    i know this is possible to find with iteration, but is it possible to find it algebraically?
     
  2. jcsd
  3. Jul 16, 2009 #2

    tiny-tim

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    Hi 3hlang! :smile:
    Nope!
     
  4. Jul 16, 2009 #3

    HallsofIvy

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    This probably isn't what you mean by "algebraically" but if you take the logarithm of both sides of the equation you get ln(y)= xln(x) and then x= W(ln(y)) where W is the "Lambert W function" which is defined as the inverse function to xln(x).
     
  5. Jul 16, 2009 #4
    ... and the reason we talk about the Lambert W function is that none of the previously-defined standard functions would work.
     
  6. Jul 22, 2009 #5
    so if x=y^y, then y=?
     
  7. Jul 22, 2009 #6

    HallsofIvy

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    All you have done is swap x and y! If [itex]x= y^y[/itex] then, by the same formula I gave before, y= W(ln(x)).
     
  8. Jul 22, 2009 #7
    what? i wasn't claiming to have done anything radical to the formula. all i wanted to know was what you do the w function of. but thank you for telling me
     
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