Question

Решите уравнение: $3log^{2} _{4} x-7log _{4} x+2=0$

Answer 1

$3log^{2} _{4} x-7log _{4} x+2=0 \\ log_{4}(x) = t \\ 3 {t}^{2} - 7t + 2 = 0 \\ d = (-7)(-7) - 4 \times 3 \times 2 = 49 - 24 = 25 \\ t1 = \frac{7 + 5}{2 \times 3} = 2 \\ t2 = \frac{7 - 5}{6} = \frac{1}{3} \\ log_{4}(x) = t$
$log_{4}(x) = 2 \\ x = {4}^{2} \\ x = 16$
и
$log_{4}(x) = \frac{1}{3 } \\ x = {4}^{ \frac{1}{3} } \\ x = \sqrt[3]{4}$
Ответ:
$x = \sqrt[3]{4}$
и
$x = 16$

Answer 2

Ответ:приложено

Объяснение: