Log1/9 (2x^2-2x-1) = - 1/2

ОДЗ:

x² - x - 2 > 0

D = 1 + 8 = 9

x₁ = (1-3) / 2 = - 1

x₂ = (1+3) / 2 = 2

x∈ (-∞; - 1) U (2; +∞)

т. к. основание меньше 1, то меняем знак:

x² - x - 2 < (1/2) ^ (-2) = 2² = 4

x² - x - 6 < 0

D = 1 + 24 = 25

x₁ = (1-5) / 2 = - 2

x₂ = (1+5) / 2 = 3

x∈ (-2; 3)

С учетом ОДЗ:

x∈ (2; 3)