solve-for-x-4x-2-x-

Question Number 34792 by mondodotto@gmail.com last updated on 11/May/18

solve for x

4 x = 2^{x}

Answered by Joel579 last updated on 11/May/18

Commented by Joel579 last updated on 11/May/18

Real solution

x = 0.3099

x = 4

Answered by mr W last updated on 13/Jan/19

4 x = e^{x \ln 2}

{x e}^{- x \ln 2} = \frac{1}{4}

(- x \ln 2) e^{- x \ln 2} = - \frac{\ln 2}{4}

\Rightarrow - x \ln 2 = W (- \frac{\ln 2}{4})

\Rightarrow x = - \frac{W (- \frac{\ln 2}{4})}{\ln 2} = {\begin{cases} - \frac{- 0.2148}{\ln 2} = 0.3099 \\ - \frac{- 2.7726}{\ln 2} = 4 \end{cases}

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