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How to solve for x in 36=X^X?

  1. Jan 25, 2012 #1
    I came up with an idea for an equation, which follows: 36=X^X. I tried solving it, but I couldn't. I found the graphically (3.15, if I recall correctly), but I want to know if there's a way to solve it algebraically.
  2. jcsd
  3. Jan 25, 2012 #2


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    nope! :redface:
  4. Jan 25, 2012 #3

    Char. Limit

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    Actually, you can, but you need to use the Lambert-W Function.
  5. Jan 26, 2012 #4
    Let f(x):=x[itex]^{x}[/itex] - 36, (f(x) is continuous, f(3.1) < 0, f(3.2) > 0) we can apply

    the 'half intervall' function I implemented in my ARIBAS_W workbench, to find the zero of f(x)

    in the intervall (3.1,3.2) as: 3.13564239388907368
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