Răspuns:
Explicație pas cu pas:
a) 3²ⁿ⁺¹⁷ x 3³ = 9²⁵
3⁽²ⁿ⁺¹⁷⁺³⁾ = 3²ˣ²⁵ ⇒ 2n + 20 = 50
2n = 50 - 20
2n = 30
n = 30 : 2
n = 15
_______________________________________________
b) (6ⁿ)⁴ x 36 = 216¹⁰
6⁴ⁿx 6² = 6³ˣ¹⁰
6⁽⁴ⁿ⁺²⁾ = 6³⁰ ⇒ 4n+2 = 30
4n = 30 - 2
n = 28 : 4
n = 7
________________________________
c) 15ⁿ⁺⁴ : 5ⁿ⁺⁴ = 81⁶
(3x5)ⁿ⁺⁴ : 5ⁿ⁺⁴ = 3⁴ˣ⁶
3⁽ⁿ⁺⁴⁾x5⁽ⁿ⁺⁴⁾ : 5⁽ⁿ⁺⁴⁾ = 3²⁴
3ⁿ⁺⁴ = 3²⁴⇒ n + 4 = 24
n = 24 - 4
n = 20
________________________
d) 81ⁿ : 9ⁿ + 9ⁿ⁺² : 9 = 90 x 9⁶
9²ⁿ⁻ⁿ + 9ⁿ x 9²⁻¹ = 9x10x9⁶
9ⁿ + 9ⁿ x 9 = 10 x 9¹⁺⁶
9ⁿ x ( 1+9) = 10x9⁷ l : 10
9ⁿ = 9⁷⇒ n = 7
______________________________________________
e) (4ⁿ⁺³)² x 8ⁿ = 32 x (8¹⁴)²
(2²ˣ⁽ⁿ⁺³⁾)² x 2³ⁿ = 2⁵x2³ˣ¹⁴ˣ²
2⁴ⁿ⁺¹²x 2³ⁿ= 2⁽⁵⁺⁸⁴⁾
2⁴ⁿ⁺¹²⁺³ⁿ = 2⁸⁹
2⁷ⁿ⁺¹² = 2⁸⁹ ⇒ 7n+12=89
7n = 89 - 12
7n = 77
n = 77 : 7
n = 11
