 The strong three exponentials conjecture meanwhile states that if "x"1, "x"2, and "y" are non-zero complex numbers with "x"1"y", "x"2"y", and "x"1/"x"2 all transcendental, then at least one of the three numbers "x"1"y", "x"2"y", "x"1/"x"2 is not in "L"∗.As with the other results in this family, the strong three exponentials conjecture implies the sharp three exponentials conjecture which implies the three exponentials conjecture.However, the strong and sharp three exponentials conjectures are implied by their four exponentials counterparts, bucking the usual trend.