Given 3 log x + $\dfrac{1}{2}$ log y = 2, express y in terms of x.

Given,

$\Rightarrow \text{3 log x} + \dfrac{1}{2} \text{log y} = 2 \\[1em] \Rightarrow \text{log } x^3 + \text{log } y^{\dfrac{1}{2}} = 2 \\[1em] \Rightarrow \text{log } x^3\sqrt{y} = 2 \\[1em] \Rightarrow x^3\sqrt{y} = 10^2$

Squaring both sides, we get :

$\Rightarrow (x^3\sqrt{y})^2 = (10^2)^2 \\[1em] \Rightarrow x^6y = 10^4 \\[1em] \Rightarrow y = \dfrac{10^4}{x^6} = 10000x^{-6}.$

Hence, y = 10000x^-6.