 The strong six exponentials theorem then says that if "x"1, "x"2, and "x"3 are complex numbers that are linearly independent over the algebraic numbers, and if "y"1 and "y"2 are a pair of complex numbers that are also linearly independent over the algebraic numbers then at least one of the six numbers "x""i" "y""j" for 1 ≤ "i" ≤ 3 and 1 ≤ "j" ≤ 2 is not in "L"∗.This is stronger than the standard six exponentials theorem which says that one of these six numbers is not simply the logarithm of an algebraic number.There is also a strong five exponentials conjecture formulated by Michel Waldschmidt It would imply both, the strong six exponentials theorem and the sharp five exponentials conjecture.