Find the value of n if a. 5 n+1+ 5 n+2 25n+5 2n+1 = 125
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Given : 5²ⁿ⁺¹ ÷ 25 = 125
To Find : Value of n
Solution:
5²ⁿ⁺¹ ÷ 25 = 125
Multiplying both sides by 25
=> 5²ⁿ⁺¹ = 25 x 125
25 = 5x 5 = 5²
125 = 5 x 5 x5 = 5³
=> 5²ⁿ⁺¹ = 5² x 5³
xᵃ * xᵇ = xᵃ⁺ᵇ
=> 5²ⁿ⁺¹ = 5²⁺³
=> 5²ⁿ⁺¹ = 5⁵
Equating powers
2n + 1 = 5
=> 2n = 4
=> n = 2
Value of n = 2
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