Решение
1) log₂ 6 + log₂ 3 - log₂ 9 = log₂(6*3)/9 = log₂ 2 = 1
Ответ: 2) 2
2) log₃ x = - 2
ОДЗ: x > 0
x = 3⁻²
x = 1/9
Ответ: 3) (0;1)
3) 2log₄² x - log₄x - 1 = 0
ОДЗ x > 0
log₄ x = t
2t² - t - 1 = 0
D = 1 + 4*2*1 = 9
t₁ = (1 - 3)/4
t₁ = - 1/2
t₂ = (1 + 3)/4
t₂ = 1
1) log₄ x = - 1/2
x = 4⁻¹/²
x₁ = 1/2
2) log₄ x = 1
x = 4¹
x₂ = 4
x₁ + x₂ = 1/2 + 4 = 4,5
Ответ: 2) 4,5