5. Решите уравнение: B) log 0.22 x + log 0.2 x − 6 = 0

В) log_(0.2)^2(x) + log_(0.2)(x) - 6 = 0 Пусть y = log_(0.2)(x), тогда уравнение принимает вид: y^2 + y - 6 = 0 D = 1^2 - 4 * 1 * (-6) = 1 + 24 = 25 y1 = (-1 + sqrt(25)) / 2 = (-1 + 5) / 2 = 4 / 2 = 2 y2 = (-1 - sqrt(25)) / 2 = (-1 - 5) / 2 = -6 / 2 = -3 1) log_(0.2)(x) = 2 x = (0.2)^2 = (1/5)^2 = 1/25 = 0.04 2) log_(0.2)(x) = -3 x = (0.2)^(-3) = (1/5)^(-3) = 5^3 = 125 Ответ: x = 0.04; x = 125