Question Number 164372 by mathlove last updated on 16/Jan/22
Commented by mathlove last updated on 16/Jan/22
$${Domain}\:{f}\left({x}\right)=? \\ $$
Answered by mahdipoor last updated on 16/Jan/22
$$\sqrt{{ln}\sqrt{{ln}\sqrt{{ln}\sqrt{{x}}}}}>\mathrm{0}\Rightarrow{ln}\sqrt{{ln}\sqrt{{ln}\sqrt{{x}}}}>\mathrm{0} \\ $$$$\Rightarrow\sqrt{{ln}\sqrt{{ln}\sqrt{{x}}}}>\mathrm{1}\Rightarrow{ln}\sqrt{{ln}\sqrt{{x}}}>\mathrm{1} \\ $$$$\Rightarrow\sqrt{{ln}\sqrt{{x}}}>{e}\Rightarrow{ln}\sqrt{{x}}>{e}^{\mathrm{2}} \\ $$$$\Rightarrow\sqrt{{x}}>{e}^{{e}^{\mathrm{2}} } \Rightarrow{x}>{e}^{\mathrm{2}{e}^{\mathrm{2}} } \\ $$