x-2-4-x-x-

Question Number 170117 by mathlove last updated on 16/May/22

x^{2} = 4^{x} x = ?

Commented by mathlove last updated on 16/May/22

x^{2} = 4^{x}

s o l v e t h i s b e f o r I m f a l l

Answered by mr W last updated on 16/May/22

x^{2} = 2^{2 x}

x = \pm 2^{x}

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

(- x \ln 2) e^{- x \ln 2} = \pm \ln 2

- x \ln 2 = W (\pm \ln 2)

f o r x \in R :

\Rightarrow x = - \frac{W (\ln 2)}{\ln 2} \approx - \frac{0.44443609}{\ln 2} = - 0.641186

Commented by mathlove last updated on 17/May/22

t h a n k s