2-x-x-2-x-2-x-4-x-0-76666-solution-please-

Question Number 184376 by Ml last updated on 05/Jan/23

2^{x} = x^{2}

x = 2

x = 4

x = - 0.76666

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solution please

Answered by Frix last updated on 05/Jan/23

2^{x} = x^{2}

x = - \frac{2 t}{\ln 2}

\Rightarrow

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

t e^{t} = \pm \frac{\ln 2}{2}

t = W (\pm \frac{\ln 2}{2}) = {\begin{cases} \ln \frac{1}{4} \lor \ln \frac{1}{2} \\ \approx . 265705736221 \end{cases}

\Rightarrow

x = {\begin{cases} 4 \lor 2 \\ \approx - . 766664695962 \end{cases}

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