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
