Question

Решите уравнение (см.внутри)

Answer 1

$log ^{2} _{3}(x) - 4 log_{3}(x) = - 3$
ОДЗ:
$x > 0$

$log {}^{2} _{3}(x) - 4 log_{3}(x) + 3 = 0 \\ log_{3}(x) = t \: \: \: \: \: t > 0 \\ {t}^{2} - 4t + 3 = 0 \\ d = 16 - 12 = 4 = {2}^{2} \\ t = \frac{4 + 2}{2} = 3 \\ t = \frac{4 - 2}{2} = 1 \\ log_{3}(x) = 1 \\ x = 3 \\ log_{3}(x) = 3 \\ x = 27$