Question

Вычислите: log ₁ ₆log√ ₂log ₃81

Answer 1

Ответ:

= 1/2=0,5

Объяснение:

$log_{16} log_{ \sqrt{2} } log_{3}81 = log_{16} log_{ \sqrt{2} } log_{3} {3}^{4} = log_{16} log_{ \sqrt{2} }(4 \times log_{3}3) = log_{16} log_{ \sqrt{2} }(4 \times 1) = log_{16} log_{ \sqrt{2} }4 = log_{16} log_{ {2}^{ \frac{1}{2} } }4 = log_{16}{((1 \div \frac{1}{2}) \times log_{2} {2}^{2} } )= log_{16}(2 \times 2 \times log_{2}2) = log_{16}4 = log_{ {4}^{2} }4 = (1 \div 2) \times log_{4}4 = \frac{1}{2} \times 1 = \frac{1}{2}$