HELLLLLLLLLLLLLLLLP

I think this might mean:   

2^x = 256^(1/2)

in which case:

2^x = 16

x = 4

.

${2}^{2}x+256+\frac{1}{2}$

$4x+256+\frac{1}{2}$

$4x+\frac{512}{2}+\frac{1}{2}$

$4x+\frac{513}{2}$

$4x+256.5$

x=-4 or x=4