1-2-x-log-1-2-x-find-x-

Question Number 143438 by Rankut last updated on 14/Jun/21

{(\frac{1}{2})}^{x} = {l o g}_{\frac{1}{2}} x

f i n d x

Answered by mr W last updated on 14/Jun/21

x = {(\frac{1}{2})}^{{(\frac{1}{2})}^{x}}

x = {(\frac{1}{2})}^{x} = e^{- x \ln 2}

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

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

\Rightarrow x = \frac{W (\ln 2)}{\ln 2} \approx \frac{0.444439091}{\ln 2} = 0.64119

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