2-1-x-x-Find-x-

Question Number 42550 by Cheyboy last updated on 27/Aug/18

2^{\frac{1}{x}} = \sqrt{x}

F i n d x

Commented by tanmay.chaudhury50@gmail.com last updated on 28/Aug/18

Commented by tanmay.chaudhury50@gmail.com last updated on 28/Aug/18

Commented by tanmay.chaudhury50@gmail.com last updated on 28/Aug/18

x = 2

Answered by MrW3 last updated on 28/Aug/18

x > 0

2^{\frac{2}{x}} = x

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

\frac{1}{x} e^{\frac{2}{x} \ln 2} = 1

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

\Rightarrow \frac{2}{x} \ln 2 = W (2 \ln 2)

\Rightarrow x = \frac{2 \ln 2}{W (2 \ln 2)} = \frac{2 \ln 2}{0.6931} = 2

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