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Question Number 7138 by Tawakalitu. last updated on 12/Aug/16

Answered by Yozzii last updated on 13/Aug/16

$$x^{x^2}=3(x>0)$$$$Let{x}^2=e^k\Rightarrow x=e^{k/2}$$$$\therefore e^{\left(k/2\right)e^k}=3$$$$\Rightarrow \frac{k}{2}{e}^k=ln3$$$${ke}^k=2ln3$$$$\Rightarrow W\left({ke}^k\right)=W\left(ln9\right)$$$$\Rightarrow k=W\left(ln9\right)$$$$\Rightarrow 2lnx=W\left(ln9\right)$$$$x=e^{\frac{1}{2}W\left(ln9\right)}$$

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