Log₄²x + log₄√x - 1,5 = 0 ОДЗ: x > 0
log₄²x + 1/2log₄x - 1,5 = 0
Умножим обе части на 2
2log₄²x + log₄x - 3 = 0
log₄x = m
2m² + m - 3 = 0
D = 1² - 4 * 2 * (-3) = 1 + 24 = 25
m ₁ = (- 1 + √25)/4 = (- 1 + 5)/4 = 1
m₂ = (- 1 - √25)/4 = (- 1 - 5)/4 = - 1,5
log₄x₁= 1 log₄x₂ = - 1,5
x₁ = 4¹ = 4