If `25^(n-1) + 100 = 5^ (2n-1)`, find the value of n :

Explanation

`25^(n-1) + 100 = 5^ (2n-1)`
`100=5^(2n-1)-25^(n-1)`
`100=5^(2n-1)-(5^2)^(n-1)`
`100=5^(2n-1)-5^(2n-2)`
`100=5^(2n)/5-5^(2n)/5^2`
`100=5^(2n)/5-5^(2n)/25`
`100=5^(2n)(1/5-1/25)`
`100=5^(2n)((5-1)/25)`
`(100xx25)/4=5^(2n)`
`625=5^(2n)`
`5^4=5^(2n)`
`4=2n`
`n=2`