Solve-for-x-2-2x-4-x-2-

Question Number 54473 by Tawa1 last updated on 04/Feb/19

Solve for x : 2^{2 x - 4} = x^{2}

Answered by mr W last updated on 04/Feb/19

{(2^{x - 2})}^{2} = x^{2}

2^{x - 2} = \pm x

\frac{1}{4} 2^{x} = \pm x

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

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

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

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

\Rightarrow x = - \frac{1}{\ln 2} W (\pm \frac{\ln 2}{4}) = {\begin{cases} - 0.2153 \\ 0.3099 \\ 4 \end{cases}

Commented by Tawa1 last updated on 04/Feb/19

God bless you sir

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