It-is-given-that-x-2-2-x-Find-x-

Question Number 96321 by Mathudent last updated on 31/May/20

I t i s g i v e n t h a t x^{2} = 2^{x} . F i n d x .

Commented by bemath last updated on 31/May/20

look qn 96241

Answered by selea last updated on 31/May/20

2^{x} = x^{2}

\ln (2^{x}) = \ln (x^{2})

xln (2) = 2 \ln ∣ x ∣

\frac{lnx}{x} = \frac{l}{2} \ln (2)

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

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

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

since

w ({xe}^{x}) = x where w () is lambert function

w (- {lnxe}^{- lnx}) = w (- \ln \sqrt{2})

lnx = - w (- \ln \sqrt{2})

x = e^{- w (- \ln \sqrt{2})} for x > 0

Commented by Mathudent last updated on 31/May/20

C a n y o u s o l v e w i t h o u t u s i n g D e l^{'} A m b e r t f u n c t i o n ?

Commented by selea last updated on 31/May/20

U can use Newton Raphson Method

Commented by mr W last updated on 31/May/20

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