Question

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$Log 4 \sqrt[5]{ \sqrt{8} }$

Answer 1

Olá!

$\\ \log_4 \sqrt[5]{\sqrt{8}} = \\\\ \log_4 \sqrt[5\cdot2]{8} = \\\\ \log_4 \sqrt[10]{8} = \\\\ \log_4 8^{\frac{1}{10}} = \\\\ \log_{2^2} (2^3)^{\frac{1}{10}} = \\\\ \frac{1}{2} \cdot \log_2 2^{\frac{3}{10}} = \\\\ \frac{1}{2} \cdot \frac{3}{10} \cdot \log_2 2 = \\\\ \frac{3}{20} \cdot 1 = \\\\ \boxed{\frac{3}{20}}$