x-x-16-find-the-value-of-x-please-show-workings-

Question Number 9392 by tawakalitu last updated on 04/Dec/16

x^{x} = 16

find the value of x .

please show workings .

Answered by mrW last updated on 04/Dec/16

using Lambert W function

x^{x} = 16

\Rightarrow xln x = \ln 16

let x = e^{u}

{ue}^{u} = \ln 16

\Rightarrow u = W (\ln 16)

\Rightarrow x = e^{W (\ln 16)} = \frac{\ln 16}{W (\ln 16)}

\approx \frac{2.77258872223978}{W (2.77258872223978)}

\approx \frac{2.77258872223978}{1.0099151364912}

\approx 2.74536802356749

Commented by tawakalitu last updated on 04/Dec/16

i really appreciate sir . God bless you .