= Baker lower bound for a homogeneous linear form in logarithms
{c}
{wiki=Baker's_theorem}
Choose logarithms of nonzero algebraic numbers $\alpha_1,\ldots,\alpha_n$, put
$$
\Lambda=\sum_{i=1}^n b_i\log\alpha_i,
\qquad b_i\in\mathbb Z,
$$
and choose $A_i\geq10$ large enough to bound the <naive polynomial height> of the minimal polynomial of $\alpha_i$ and $\exp(|\log\alpha_i|)$. After relabelling the terms if useful, set
$$
B^*=\max\left(\frac{|b_1|}{\log A_n},\ldots,
\frac{|b_{n-1}|}{\log A_n},|b_n|,10\right).
$$
There is an effectively computable constant $C$, depending only on $n$ and the degree of the number field generated by the $\alpha_i$, such that
$$
\Lambda\ne0
\quad\Longrightarrow\quad
|\Lambda|>\exp\!\left(-C(\log A_1)\cdots(\log A_n)\log B^*\right).
$$
The division by $\log A_n$ is the useful refinement over the <general lower bound for a linear form in logarithms> when one algebraic number has a large height correlated with a coefficient.
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