Question

Find the value of n, if
(a) 5^n-1 × 3^2n-3 = 675​

Answer 1

Answer:

n = 3

Step-by-step explanation:

5ⁿ⁻¹ x 3²ⁿ⁻³ = 675

5ⁿ⁻¹ x 3²ⁿ⁻³ = 3³5²

5ⁿ⁻¹ = 5²

n - 1 = 2

n = 2+1

n = 3

3²ⁿ⁻³ = 3³

2n-3 = 3

2n = 3+3

2n = 6

n = 6/2

n = 3

Answer 2

Answer:

n= 3

Step-by-step explanation:

5^n-1 x 3^2n-3 = 675

5^n-1 x 3^2n-3 = 3^3+5^2

Equating powers of 5

n-1 = 2

n= 2+1

n= 3

Equating powers of 3

2n-3 = 3

2n = 3+3

n= 6/2

n= 3

Check-

5^3-1 x 3^2x3-3 = 3^3+5^2

5^2 x 3^3 = 3^3+5^2

Hence, verified

Hope you Understood