= Baker's theorem
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= Baker theorem on algebraic linear combinations of logarithms
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If chosen logarithms of algebraic numbers are linearly independent over $\mathbb Q$, then they, together with one, are linearly independent over $\overline{\mathbb Q}$. More generally a nonzero homogeneous linear combination with algebraic coefficients is transcendental. Quantitative lower bounds for integer coefficients are a separate, effective aspect of logarithmic-form theory.
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