Let x, y, and z be positive real numbers that satisfy\[2 \log_x (2y) = 2 \log_{2x} (4z) = \log_{2x^4} (8yz) \neq 0.\]the value of xy^5 z can be expressed in the form \frac{1}{2^{p/q}}, where p and q are relatively prime positive integers. find p + q.