Задача 71905 log_(5)^2 x + 3log5x - 4 = 0...

64099668438f4e0b023ada83

01.06.2023 10:35:18

log_(5)^2 x + 3log5x - 4 = 0

626fab9a354ab65fb2f43abb

01.06.2023 14:30:13

★

[m]\log^2_5(x) + 3\log_5(x) - 4 = 0[/m]
Область определения:
D(X) = (0; +oo)
Решаем заменой [m]y = \log_5(x)[/m]
y^2 + 3y - 4 = 0
(y + 4)(y - 1) = 0
[m]y1 = \log_5(x) = -4[/m]; [m]x1 = 5^{-4} = \frac{1}{5^4} = \frac{1}{625}[/m]
[m]y2 = \log_5(x) = 1[/m]; [m]x2 = 5^1 = 5[/m]

Ответ: x1 = 1/625; x2 = 5