Question

Вычислить логарифм .​

Answer 1

Ответ:

$= - \frac{11}{3} \\ = \frac{7}{12}$

Пошаговое объяснение:

$log_{ \frac{1}{3} }(9 \times \sqrt[4]{27} ) = log_{ {3}^{ - 1} }( {3}^{2} \times \sqrt[4]{ {3}^{3} } ) = (1 \div ( - 1)) \times log_{3}( {3}^{2} \times {3}^{ \frac{3}{4}}) = - 1 \times log_{3} {3}^{2 + \frac{3}{4}} = - 1 \times \frac{11}{3} \times log_{3}3 = - \frac{11}{3} \times 1 = - \frac{11}{3}$

$log_{49}(7 \times \sqrt[6]{7}) = log_{ {7 }^{2} }( {7}^{1} \times {7}^{ \frac{1}{6}} = (1 \div 2) \times log_{7}( {7}^{1 + \frac{1}{6}}) = \frac{1}{2} \times \frac{7}{6} \times log_{7}7 = \frac{7}{12} \times 1 = \frac{7}{12}$