Weak Schanuel conjecture

Let $\alpha_1,\ldots,\alpha_n$ be non-zero algebraic numbers such that the numbers $\log \alpha_1,\ldots,\log \alpha_n$ are $\mathbb{Q}$-linearly independent. Weak Schanuel conjecture. Then $\log \alpha_1,\ldots,\log \alpha_n$ are algebraically independent. This conjecture is used here to obtain conditional results on the algebraic independence of Euler–Briggs constants; its general status is open.