The Wikipedia article on Baker's theorem states it as follows:
If $\lambda_1,\ldots,\lambda_n\in\mathbb{L}$ are linearly independent over the rational numbers, then for any algebraic numbers $\beta_0,\ldots,\beta_n$, not all zero we have $$|\beta_0+\beta_1\lambda_1+\cdots+\beta_n\lambda_n|>H^{-C}$$ where $H$ is the maximum of the heights of $\beta_i$ and $C$ is an effectively computable number depending on $n$, $\lambda _{i}$ and the maximum $d$ of the degrees of $\beta_i$.
But I don't think this holds if the $\beta_i$ have height at most $1$. For example consider $|\log(2\cdot3)-\log(3)|=\log(2)<1$.
I'm assuming the height of an algebraic number $\beta$ refers to $\max_i(|a_i|)$ where the $a_i$ are the coefficients of an irreducible polynomial of $\beta$ such that the coefficients are relatively prime integers.
I've also checked Baker's book Transcendental Number Theory and in place of $H$ he uses $B\geq 2$, an upper-bound of $H$.