Решение
1) log₃ 8 + 3log₃ (9/2) = log₃ 8 + log₃ (9/2)³ = log₃ (8* (9³/8) =
= log₃ 3⁶ = 6log₃ 3 = 6
2) log₄ (1/128) = log⁴ (4⁻5) = - 5*log₄ 4 = - 5
3) 2log₇ 32 - log₇ 256 - 2log₇ 14 = log₇ 32² - log₇ 256 - log₇ 14² =
= log₇ (2¹⁰ / (2⁸ * 14²) = log₇ (2²) / (2² * 7²) = log₇ (1/7²) = log₇ 7⁻² =
= - 2*log₇ 7 = - 2
4) не видна правая часть уравнения
5) log₄ (x - 3) + log₄ (x + 3) = 2
ОДЗ: x - 3 > 0, x > 3
x + 3 > 0
x > - 3
ОДЗ: x ∈(3; + ∞)
log₄ (x² - 9) = log₄ 4²
x² - 9 = 16
x² = 25
x₁ = - 5 - не удовлетворяет ОДЗ: x ∈(3; + ∞)
x₂ = 5
Ответ: х = 5