Find the value of x : (4)2x-1-(16)x-1=384 . . .

Question : Find the value of x : (4)^2x-1-(16)^x-1=384  

Doubt by Balvinder

Solution : 

(4)^2x-1 - (16)^x-1 = 384

(4)^2x-1 - (4²)^x-1 = 384
(4)^2x-1 - (4)^2(x-1) = 384

(4)^2x-1 - (4)^2x-2 = 384

(4)^2x-1 - (4)^2x-1-1 = 384
(4)^2x-1 - (4)^2x-1.4^-1 = 384

(4)^2x-1 [1-1/4] = 384
(4)^2x-1 [(4-1)/4] = 384

(4)^2x-1 [3/4] = 384
(4)^2x-1= (384×4)/3
(4)^2x-1= 128×4
(4)^2x-1= 512
(2²)^2x-1=2⁹
2^2(2x-1)=2⁹
2^4x-2=2⁹

equating the power of 2 both sides
4x-2=9
4x=9+2
4x=11
x=11/4