Question

If 5^2x-1 -100=25^x-1,then find the value of 6^x

Answer 1

5^(2x-1) -100 = 25^(x-1)
⇒5^(2x-1) - 100 = 5^2(x-1) =5^(2x-2)
consider 5^2x be a,then
⇒a×5^(-1) -100 = a×5^(-2)
⇒a/5 -100 =a/25
⇒4a/25 =100
⇒a =625
now, 5^2x =625 =5^4
equating the powers, 
2x= 4
⇒x =2
so, 6^2 = 36