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Sagot :

Réponse :

Bonsoir

Exercice 82

1) 9²ⁿ = 3⁴ ⇔ (3²)²ⁿ = 3⁴ ⇔ 3⁴ⁿ = 3⁴ ⇔ 4n = 4 ⇔ n =1

2) 2ⁿ⁺¹ = 1/8 ⇔ 2ⁿ⁺¹ = 1/2³ ⇔ 2ⁿ⁺¹ = 2⁻³ ⇔ n + 1 = -3 ⇔ n = -4

3) (1/125)ⁿ = 5⁻²ⁿ × 125 ⇔ (1/5³)ⁿ = 5⁻²ⁿ × 5³ ⇔ 5⁻³ⁿ = 5⁻²ⁿ⁺³ ⇔ -3n = -2n +3

⇔ n = -3

Exercice 83

15³ⁿ⁺⁵ = 3²ⁿ⁺⁶ × 5⁴ⁿ⁺⁴ ⇔ 3³ⁿ⁺⁵ × 5³ⁿ⁺⁵ = 3²ⁿ⁺⁶ × 5⁴ⁿ⁺⁴

⇔ 3n +5 = 2n + 6  et 3n + 5 = 4n + 4

⇔ n = 1

Exercice 84

7(3ⁿ + 3ⁿ⁺¹ + 3ⁿ⁺²) = 21ⁿ × 13

⇔ 7 × 3ⁿ(1 + 3 + 3²) = 3ⁿ × 7ⁿ × 13

⇔ 3ⁿ × 7 × 13 = 3ⁿ × 7ⁿ × 13

n = 1

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