Question

ПОМОГИТЕ РЕШИТЬ .............................

Answer 1

Решение
log₂² (x/2) - log₂ (4x) = 3
ОДЗ: x/2 > 0, x > 0
4x > 0, x > 0
[(log₂ x) - log₂ 2]² - log₂ 4 - log₂ x = 3
log₂² x - 2log₂ x + 1 - 2 - log₂ x - 3 = 0
log₂² x - 3log₂ x - 4 = 0
log₂ x = t
t² - 3t - 4 = 0
t₁ = - 1
t₂ = 4
1)  log₂ x = - 1
x = 2⁻¹
x₁ = 1/2
2) log₂ x = 4
x = 2⁴
x₂ = 16
x₁ * x₂ = (1/2) * 16 = 8