Question

решите пж математика 10 класс логарифмы

Answer 1

Ответ:

ОДЗ: х > 0

$log_{8}(x) + log_{ \sqrt{2} }(x) = 14 \\ log_{ {2}^{3} }(x) + log_{ {2}^{ \frac{1}{2} } }(x) = 14 \\ \frac{1}{3} log_{2}(x) + 2 log_{2}(x) = 14 \\ ( \frac{1}{3} + 2) log_{2}(x) = 14 \\ \frac{7}{3} log_{2}(x) = 14 \\ log_{2}(x) = 14 \times \frac{3}{7} \\ log_{2}(x) = 6 \\ x = {2}^{6} = 64$