Question

Прологарифмируйте выражение по заданному основанию 2.

Answer 1

$log_{2}( \frac{ \sqrt[3]{8} \sqrt[4]{8} }{ \sqrt{24} } ) = \\ = log_{2}( \frac{ {2}^{3 \times \frac{1}{3} + \frac{1}{4} } }{\sqrt{ {2}^{3} } \sqrt{3} } ) = \\ = log_{2}( \frac{ {2}^{ \frac{5}{4} } }{\sqrt{ {2}^{3} } \sqrt{3} } ) = \\\\ = log_{2}( \frac{ {2}^{ \frac{5}{4} - \frac{1}{3} } }{ \sqrt{3} } ) = \\ = log_{2}( {2}^{ \frac{11}{12} } ) - log_{2}( { 3}^{ \frac{1}{2} } ) = \\ = \frac{11}{12} log_{2}2 - \frac{1}{2} log_{2}3 = \\ = \frac{11}{12} - \frac{1}{2} log_{2}3$