log ab = log a + log b
(log(5) (125x)*log(3) (81x)) / (x² - |x|) ≤ 0
одз 125x > 0 x > 0
81x > 0 x > 0
x² - |x| ≠ 0 x ≠ 0 x ≠ -1 x ≠ 1
x∈(0, 1) U (1, +∞)
так как x > 0 модуль снимаем как х
((log(5) (125) + log(5) x)*(log(3) (81) + log(3) x) / x(x - 1) ≤ 0
81 = 3^4
125 = 5^3
(3 + log(5) x)(4 + log(3) x) / x(x - 1) ≤ 0
log(5) x = -3 x = 5^(-3) = 1/125
log(3) x = -4 x = 3^(-4) = 1/81
(0) [1/125][1/81](1)
x ∈ (0, 1/125] U [ 1/81, 1)
log ab = log a + log b
(log(5) (125x)*log(3) (81x)) / (x² - |x|) ≤ 0
одз 125x > 0 x > 0
81x > 0 x > 0
x² - |x| ≠ 0 x ≠ 0 x ≠ -1 x ≠ 1
x∈(0, 1) U (1, +∞)
так как x > 0 модуль снимаем как х
((log(5) (125) + log(5) x)*(log(3) (81) + log(3) x) / x(x - 1) ≤ 0
81 = 3^4
125 = 5^3
(3 + log(5) x)(4 + log(3) x) / x(x - 1) ≤ 0
log(5) x = -3 x = 5^(-3) = 1/125
log(3) x = -4 x = 3^(-4) = 1/81
(0) [1/125][1/81](1)
x ∈ (0, 1/125] U [ 1/81, 1)