$$a ^ { x } = b ^ { y } = c ^ { z } b ^ { 2 } = a c , y = \frac { 2 x z } { z + x }$$
$a^{x}=b^{y}\text{ and }b^{y}=b^{2}c^{z}\text{ and }b^{2}c^{z}=ac,y=\frac{2xz}{x+z}$
