Solve the following equation for x:

log₈₁x = $\dfrac{3}{2}$

Given,

⇒ log₈₁x = $\dfrac{3}{2}$

$\Rightarrow x = (81)^{\dfrac{3}{2}} \\[1em] \Rightarrow x = (9)^2{\dfrac{3}{2}} \\[1em] \Rightarrow x = 9^3 = 729.$

Hence, x = 729.