If 25^n-1+100=5^2n-1 then find the value of n ?

With process

25^n-1 + 100 = 5^2n-1

25^n.25^-1 + 100= 5^2n.5^-1

25^n.25^-1 + 100= 25^n.5^-1

Now take 25^n.25^-1 part to RHS then will get

25^n.5^-1 - (25^n.25^-1 )=100

Now take 25^n common from LHS

25^n(1/5 - 1/25)= 100

25^n(4/25)=100

25^n=100*25/4

25^n=25*25

25^n=25^2

Now we can say that

n=2.