lim-x-3-log-2log-x-3-2-1-3-1-4-

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

\lim_{x \to 3} [\sqrt[4]{l o g \sqrt[3]{2 l o g \sqrt{x^{3} + 2}}}] = ?

Answered by alephzero last updated on 23/Mar/22

\lim_{x \to 3} \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}