Solve the following equation for x:

log₄x = -1.5

Given,

⇒ log₄x = -1.5

⇒ x = 4^-1.5

⇒ x = $4^{-\dfrac{3}{2}} = (2^2)^{-\dfrac{3}{2}}$

⇒ x = 2^-3 = $\dfrac{1}{2^3} = \dfrac{1}{8}$.

Hence, x = $\dfrac{1}{8}$.