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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.
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