Find the value of n if (i) 5^(n-2) x 3^(2n-3) = 135 and (ii) 100 + 25^(n-1)=5^(2n-1)​

Question

Find value of n

(i) 5^(n-2) x 3^(2n-3) = 135

(ii) 100 + 25^(n-1) = 5^(2n-1)​

Answer 1

The solution for question (i):

The solution for question (ii):

25^(n-1) + 100= 5^2n-1

given equation is:

let 5^2n-1 = t , therefore, the above equation becomes:

t+100=5t

5t-t=100

4t=100

t=100/4=25

hence, 5^2n-2=25=5²

Since the base is same comparing the exponents:

2n-2=2

2n=2+2=4

n=4/2 = 2

n=2