We have to solve 1/1024 = 4*16^2x for x.

1/1024 = 4*16^2x

=> 1/(2^10) = (2^2)*(2^4^2x)

=> 1/(2^10) = (2^2)*(2^8x)

=> [1/(2^10)]/(2^2) = (2^8x)

=> 2^(-10 - 2) = (2^2)*(2^8x)

=> 2^-12 = (2^8x)

As the base is the same we equate the exponent.

-12 = 8x

=> x = -12/8

=> x = -3/2

**The required value is x = -3/2**