If $\dfrac{\text{log x}}{2} = \dfrac{\text{log y}}{3}$, find the value of $\dfrac{y^4}{x^6}$.

Given,

$\dfrac{\text{log x}}{2} = \dfrac{\text{log y}}{3}$

⇒ 3log x = 2log y

⇒ log x³ = log y²

⇒ x³ = y²

Squaring both sides we get,

⇒ x⁶ = y⁴

⇒ $\dfrac{x^6}{y^4} = 1$.

Hence, $\dfrac{x^6}{y^4} = 1$.