8. Воспользуйтесь свойствами логарифмов и решите уравнение log3 (3 - x) + log3 (4 - x) = 1 + 2log3 2.

Ответ: x = -1

log₃ (3 - x) + log₃ (4 - x) = 1 + 2log₃ 2

log₃ ((3 - x) * (4 - x)) = log₃ 3 + log₃ 2²

log₃ (12 - 7x + x²) = log₃ (3 * 4)

x² - 7x + 12 = 12

x² - 7x = 0

x(x - 7) = 0

x₁ = 0

x₂ = 7

Проверим корни:

3 - x > 0 => x < 3

4 - x > 0 => x < 4

x = 0 подходит

x = 7 не подходит

log₃ (3 - x) + log₃ (4 - x) = 1 + 2log₃ 2

log₃ (3 - x)(4 - x) = log₃ 3 + log₃ 2²

log₃ (12 - 7x + x²) = log₃ 12

12 - 7x + x² = 12

x² - 7x = 0

x(x - 7) = 0

x₁ = 0

x₂ = 7

Проверим:

x = 0

log₃ 3 + log₃ 4 = 1 + 2log₃ 2

1 + log₃ 4 = 1 + log₃ 4

x = 7

log₃ (-4) + log₃ (-3)

Ответ: x = -1