1/2^x=16^(x+4)

(1/2)^x  =  (16)^x+4

If we get all of these to the same base, we can get a simple equation that we can solve ---

(1/2)  =  2^-1         (16)  =  (2)⁴

Substituting these, we get:

(2^-1)x  =  (2⁴)^{x+ 4}

Simplifying, we get:

2^-x  =  2^{4x + 16}

Since the bases are the same, the exponents must be equal:

-x  =  4x + 16   --->   -5x  =  16   --->   x  =  -16/5