If 5^2x-1-25^x-1=2500, find the value . . .

Question : If 5^2x-1-25^x-1=2500, find the value of x.

Doubt by Bhumika

Solution : 

5^2x-1-25^x-1=2500
5^2x-1-(5²)^x-1=2500
5^2x-1-5^2x-2=2500
5^2x-1-5^2x-1-1=2500
5^2x-1-5^2x-1÷5¹=2500
5^2x-1(1-1/5)=2500
5^2x-1(4/5)=2500
5^2x-1=[2500×5]/4
5^2x-1=3125
5^2x-1=5⁵
Comparing the exponents both sides
2x-1=5
2x=5+1
2x=6
x=6/2
x=3