Question

Cat însemna logaritm de baza 2 din 4 radical de ordin 3 din 2? Va rog mult, mulțumesc! ​

Answer 1

$4 \sqrt[3]{2} = {2}^{2} \sqrt[3]{2} = \sqrt[3] { {2}^{6} \times 2 } = \\ \sqrt[3]{ {2}^{7} } = 2 {}^{ \frac{7}{3} }$

$log_{2}(4 \sqrt[3]{2} ) = log_{2}(2 {}^{ \frac{7}{3} } ) = \\ = \frac{7}{3} \times log_{2}(2) = \\ = \frac{7}{3} \times 1 = \frac{7}{3}$