Given that \(\log _ { 3 } c = m\) and \(\log _ { 27 } d = n\), express \(\frac { \sqrt { c } } { d ^ { 2 } }\) in the form \(3 ^ { y }\), where \(y\) is an expression in terms of \(m\) and \(n\).
Show that the equation
$$\log _ { 4 } ( 2 x + 3 ) + \log _ { 4 } ( 2 x + 15 ) = 1 + \log _ { 4 } ( 14 x + 5 )$$
has only one solution and state its value.