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Math Help - Solve in R

  1. #1
    Super Member dhiab's Avatar
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    Solve in R

    Solve in R :

    x^{x^{\frac{1}{2}}}=\frac{1}{2}
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  2. #2
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    Re: Solve in R

    see below

    Solve in R-12345.png
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  3. #3
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    Re: Solve in R

    The analytic solution of x^sqrt(x)=1/2 is
    x=exp(2*W(-ln(2)/2)) where W is the LambertW function.
    The LambertW function is multi-valuated. Numerical evalation leads to
    x=0.25 and x=0.0625
    Of course, the values can be found much more simply, by direct evalation.
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