 The strongest result that has been conjectured in this circle of problems is the strong four exponentials conjecture.This result would imply both aforementioned conjectures concerning four exponentials as well as all the five and six exponentials conjectures and theorems, as illustrated to the right, and all the three exponentials conjectures detailed below.The statement of this conjecture deals with the vector space over the algebraic numbers generated by 1 and all logarithms of non-zero algebraic numbers, denoted here as "L"∗.