Log3 x* log0,2 x=4log0.2 3

Решите задачу:

$log_3(x) * log_{0,2}(x) = log_{0,2}(3) \\ log_{3}(x) * \frac{log_3(x)}{log_3(0,2)} = log_{0,2}(3) \\ \frac{log_3(x) * log_3(x)}{log_3(0,2)} = log_{0,2}(3) \\ \frac{log_3(x)^2}{log_3(0,2)} = log_{0,2}(3) \\ log_3(x)^2 = log_{0,2}(3) * log_3{(0,2)} \\ log_3(x)^2 = \frac{log_3(3)}{log_3(0,2)} * log_3(0,2) \\ log_3(x)^2 = \frac{1}{log_3(0,2)} * log_3{0,2} \\ log_3(x)^2 = 1 \\ log_3(x)^2 =+- \sqrt{1} \\ log_3(x)=1 \\ log_3(x)=-1 \\ x_1=3^1=3 \\ x_2=3^{-1}= \frac{1}{3} \\$