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2.
3⁵ˣ⁻¹ = 27ˣ⁺³
3⁵ˣ⁻¹ = (3³)ˣ⁺³
3⁵ˣ⁻¹ = 3³ˣ⁺⁹
5x - 1 = 3x + 9
2x = 10
x = 5
3.
3ˣ²⁺ˣ⁻² = 81ˣ⁺²
3ˣ²⁺ˣ⁻² = (3⁴)ˣ⁺²
3ˣ²⁺ˣ⁻² = 3⁴ˣ⁺⁸
x² + x - 2 = 4x + 8
x² - 3x - 10 = 0
(x - 5)(x + 2) = 0
x = 5 v x = -2
x1 - x2 = 5 - (-2) = 5 + 2 = 7
4.
2ˣ . 8ˣ⁻¹ = 32
2ˣ . (2³)ˣ⁻¹ = 2⁵
2ˣ . 2³ˣ⁻³ = 2⁵
2ˣ⁺³ˣ⁻³ = 2⁵
x + 3x - 3 = 5
4x = 8
x = 2
6.
∛8ˣ⁺² = (1/32)²⁻ˣ
∛(2³)ˣ⁺² = (2⁻⁵)²⁻ˣ
2ˣ⁺² = 2⁻¹⁰⁺⁵ˣ
x + 2 = -10 + 5x
4x = 12
x = 3
8x - x² = 24 - 9 = 15