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b)3^(2n-3)=27⁷:9²

3^(2n-3)=3¹⁷

2n-3=17

2n=17+3

2n=20

n=20:2

n=10

c)5^(3n+1)=25¹¹

5^(3n+1)=5²²

3n+1=22

3n=22-1

3n=21

n=21:3

n=7

d)7^(n+1):7⁴=49²^³

7^(n-3)=7²^⁴

n-3=2⁴

n-3=16

n=16+3

n=19

e)10^(2n+1):5^(2n+1)=8⁹

2^(2n+1)×5^(2n+1):5^(2n+1)=2²⁷

2^(2n+1)×1=2²⁷

2^(2n+1)=2²⁷

2n+1=27

2n=27-1

2n=26

n=26:2

n=13

Răspuns:

Explicație pas cu pas:

b) 3²ⁿ⁻³ = 27⁷:9² <=> 3²ⁿ⁻³= (3³)⁷ :(3²)²  <=>

3²ⁿ⁻³ = 3²¹⁻⁴  <=> 3²ⁿ⁻³ = 3¹⁷ => 2n-3 = 17 <=> 2n = 20 =>

n = 20:2 => n = 10

c) 5³ⁿ⁺¹ = 25¹¹ <=> 5³ⁿ⁺¹ = (5²)¹¹ <=> 5³ⁿ⁺¹ = 5²² => 3n+1 = 22 =>

3n = 21 => n = 21:3 => n = 7

d) 7ⁿ⁺¹:7⁴ = 49²^³ <=> 7ⁿ⁺¹⁻⁴ = (7²)⁸ <=> 7ⁿ⁻³ = 7¹⁶ =>

n-3 = 16 => n = 19

e) 10²ⁿ⁺¹ : 5²ⁿ⁺¹ = 8⁹ <=> (10:5)²ⁿ⁺¹ = (2³)⁹ <=>

2²ⁿ⁺¹ = 2²⁷ => 2n+1 = 27 => 2n = 26 => n = 26:2 => n = 13