if-x-x-2-what-is-the-value-of-x-

Question Number 26269 by ibraheem160 last updated on 23/Dec/17

i f x^{x} = 2 w h a t i s t h e v a l u e o f x ?

Answered by mrW1 last updated on 23/Dec/17

x^{x} = 2

x \ln x = \ln 2

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

\Rightarrow \ln x = W (\ln 2)

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

= \frac{0.693147}{W (0.693147)} = \frac{0.693147}{0.444446} = 1.559610

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