Question

Решите пожалуйста логарифмическое уравнение на листочке.​

Answer 1

$log_{3}(x) + log_{9}(x) + log_{27}(x) = \frac{11}{12} \\ \\ log_{3}(x) + log_{ {3}^{2} }(x) + log_{ {3}^{3} }(x) = \frac{11}{12} \\ \\ log_{3}(x) + \frac{1}{2} log_{3}(x) + \frac{1}{3} log_{3}(x) = \frac{11}{12} \\ \\ ( 1 + \frac{1}{2} + \frac{1}{3} ) log_{3}(x) = \frac{11}{12} \\ \\ \frac{11}{6} log_{3}(x) = \frac{11}{12} \\ \\ log_{3}(x) = \frac{11}{12} \times \frac{6}{11} \\ \\ log_{3}(x) = \frac{1}{2} \\ \\ x = {3}^{ \frac{1}{2} } = \sqrt{3}$