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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 : \left( {x^x } \right)^2 = 8
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    Interesting question, I said x^x = \sqrt{8} then using trial and error I found x \approx 1.788454
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  3. #3
    Super Member Random Variable's Avatar
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     x^{x}= \sqrt{8} = 2^{3/2}

     e^{\ln x \ e^{\ln x}} = 2^{3/2}

     \ln (e^{\ln x \ e^{\ln x}}) = \ln (2^{3/2})

     \ln x e^{\ln x} =\frac{3}{2} \ln 2

     \ln x = \frac{\frac{3}{2}\ln 2}{e^{\ln x}} = W\Big(\frac{3}{2} \ln 2\Big)

    where W is the Lambert W function

    so x = e^{W\Big(\frac{3}{2} \ln 2\Big)} \approx 1.788
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