If (3)^x = (5)^y = (75)^z, show that $z = \dfrac{xy}{2x + y}$

Solve the following equations for x :

(i) $\sqrt{3^{x + 1}} = 27$

Solve the following equation :

$4^{2x} = (\sqrt[3]{16})^{-\frac{6}{y}} = (\sqrt{8})^2$

Solve the following equation :

3^{x - 1} × 5^{2y - 3} = 225