Question

2 * log_3(x) = 2 * log_x(3) + 3 .

Answer 1

Ответ:

$2 log_{3}x = 2 log_{x}3 + 3 \\ x > 0 \\ x \ne1 \\ 2 log_{3} x = \frac{2}{ log_{3}x} +3 \\ log_{3}x = t \\ 2t = \frac{2}{t} + 3 \\ \frac{2 {t}^{2} - 3t - 2}{t} = 0 \\ t = - 0.5 \\ t = 2 \\ log_{3 }x = - 0.5 \\ x = {3}^{ - 0.5} = \frac{1}{ \sqrt{3} } \\ log_{3}x = 2 \\ x = {3}^{2} = 9$