Solve the following equation for x:

log₄(2x + 3) = $\dfrac{3}{2}$

Given,

⇒ log₄(2x + 3) = $\dfrac{3}{2}$

⇒ 2x + 3 = $4^{\dfrac{3}{2}}$

⇒ 2x + 3 = $(2^2)^{\dfrac{3}{2}}$

⇒ 2x + 3 = 2³

⇒ 2x + 3 = 8

⇒ 2x = 5

⇒ x = $\dfrac{5}{2}$.

Hence, x = $\dfrac{5}{2}$.