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Question Number 127139 by MathSh last updated on 27/Dec/20

$$2^y=y^2\Rightarrow y=?$$

Answered by Ar Brandon last updated on 27/Dec/20

$$2$$

Commented by MathSh last updated on 27/Dec/20

$$Thanks,solutionsir$$

Answered by Dwaipayan Shikari last updated on 27/Dec/20

$$2^y=y^2\Rightarrow y=\pm 2^{\frac{y}{2}}$$$$\Rightarrow y=e^{\pm \frac{y}{2}log\left(2\right)}$$$$\Rightarrow \pm \frac{y}{2}log\left(2\right)=\frac{1}{2}{e}^{\pm \frac{y}{2}log\left(2\right)}log\left(2\right)$$$$\Rightarrow \pm \frac{y}{2}log\left(2\right)e^{\pm \frac{y}{2}log\left(2\right)}=\pm \frac{1}{2}log\left(2\right)$$$$\Rightarrow \pm \frac{y}{2}log\left(2\right)=W_0(\pm \frac{log2}{2})\Rightarrow y=\pm \frac{2W_0(\pm \frac{log2}{2})}{log\left(2\right)}$$

Commented by MathSh last updated on 27/Dec/20

$$Thankssir,answer:?$$

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