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Question Number 164372 by mathlove last updated on 16/Jan/22

Commented by mathlove last updated on 16/Jan/22

$$Domainf\left(x\right)=?$$

Answered by mahdipoor last updated on 16/Jan/22

$$\sqrt{ln\sqrt{ln\sqrt{ln\sqrt{x}}}}>0\Rightarrow ln\sqrt{ln\sqrt{ln\sqrt{x}}}>0$$$$\Rightarrow \sqrt{ln\sqrt{ln\sqrt{x}}}>1\Rightarrow ln\sqrt{ln\sqrt{x}}>1$$$$\Rightarrow \sqrt{ln\sqrt{x}}>e\Rightarrow ln\sqrt{x}>e^2$$$$\Rightarrow \sqrt{x}>e^{e^2}\Rightarrow x>e^{2e^2}$$

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