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Question Number 167662 by mathlove last updated on 22/Mar/22

$$\underset{x\to 3}{\lim }\left[\sqrt[4]{log\sqrt[3]{2log\sqrt{x^3+2}}}\right]=?$$

Answered by alephzero last updated on 23/Mar/22

$$\underset{x\to 3}{\lim }\sqrt[4]{\ln \sqrt[3]{2\ln \sqrt{x^3+2}}}=$$$$=\lim \sqrt[4]{\frac{1}{3}\ln \ln (x^3+2)}=$$$$=\sqrt[4]{\frac{1}{3}\ln \ln 29}$$

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