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Question-164372




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

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