If 3x = 5y = (75)z, Show that

$3^{x}=k$

$3=k^{1 / x}$

$5^{y}=k$

$5=k^{1 / y}$

$75^{z}=k$

$75=k^{1 / z}$

$3^{1} \times 5^{2}=75^{1}$

$k^{1 / x} \times k^{2 / y}=k^{1 / z}$

$1 / x+2 / y=1 / z$

$\frac{y+2 x}{x y}=\frac{1}{z}$

$z=\frac{x y}{2 x+y}$