2/(5^x - 1) + (5^x - 2)/(5^x - 3) ≥ 2
5^x ≠ 1 x≠0
5^x - 3 ≠ 0 x ≠ log(5) 3
(5^x - 2)/(5^x - 3) = (5^x - 3 + 1)/(5^x - 3) = 1 + 1/(5^x - 3)
2/(5^x - 1) + 1 + 1/(5^x - 3) ≥ 2
2/(5^x - 1) + 1/(5^x - 3) - 1 ≥ 0
5^x = t > 0
2/(t - 1) + 1/(t - 3) - 1 ≥ 0
(2(t - 3) + (t - 1) - (t - 1)(t - 3))/(t - 1)(t - 3) ≥ 0
(2t - 6 + t - 1 - t² + 4t - 3)/(t - 1)(t - 3) ≥ 0
(-t² + 7t - 10)/(t - 1)(t - 3) ≥ 0
(t - 2)(t - 5)/(t - 1)(t - 3) ≤ 0
(1) [2] (3) [5]
t ∈ (1, 2] U (3, 5]
5^x = t
5^x > 1
x > 0
5^x ≤ 2
x ≤ log(5) 2
5^x > 3
x > log(5) 3
5^x ≤5
x ≤ 1
ответ x ∈ (0, log(5) 2] U (log(5) 3, 1]
