Verified answer

1) take the antilog of both sides.

2^4 = x^3 -----> 16 = x^3

2) x = 16^1\3

3) x = 2(8)^1\3 or 2 cube roots of 8

4) log equation always need checked, so if x is 16^1/3 then log[base2](16^1/3)^3 = log[base2]16 which = 4.

_____________________________________

log₂x³ = 4   ⇐⇒   x³ = 2⁴

                                                  x = ∛ ̅2̅̅⁴̅̅           ← took the cube root of both sides

                                                  x = ∛ ̅1̅̅6̅̅

                                                  x = ∛ ̅8̅·̅2̅

                                                  x = ∛ ̅8̅    ∛ ̅2̅

                                                  x = 2∛ ̅2̅

__________________________________