1. 4ˣ = 16
4ˣ = 4²
x = 2.
2. 3ˣ⁺² = 27
3ˣ⁺² = 3³
x + 2 = 3
x = 1.
3. 3ˣ⁺² = 9²ˣ⁻³
3ˣ⁺² = 3⁴ˣ⁻⁶
x + 2 = 4x - 6
x - 4x = -6 - 2
-3x = -8
x = 8/3
4. log₅x = 2
5² = x
x = 25.
5. log₄(2 - x) = -2
4⁻² = 2 - x
1/16 = 2 - x
x = 2 - 1/16
x = 31/16
6. log₅(x² - 4x) = log₅(3 - 2x)
ОДЗ:
x² - 4x > 0 и 3 - 2x > 0
x(x - 4) > 0 и 2x < 3
x ∈ (-∞; 0) U (4; +∞) и x ∈ (-∞; 1,5)
x ∈ (-∞; 0)
x² - 4x = 3 - 2x
x² - 2x - 3 = 0
x² - 2x + 1 - 4 = 0
(x - 1)² - 2² = 0
(x - 1 - 2)(x - 1 + 2) = 0
(x + 1)(x - 3) = 0
x = 3 - не уд. ОДЗ; x = -1.
Ответ: x = -1.