General lower bound for a linear form in logarithms

Choose logarithms of nonzero algebraic numbers ${\alpha }_1,\dots ,{\alpha }_n$ and algebraic numbers ${\beta }_0,\dots ,{\beta }_n$, and putLet $A_j$ bound $10$, the naive polynomial height of the minimal polynomial of ${\alpha }_j$, and $\exp (|\log {\alpha }_j|)$. Let $B$ bound all the corresponding heights of the ${\beta }_j$ and all $\log A_j$. There is an effective constant $C$, depending only on $n$ and the degree of the number field generated by the data, such that