Diophantine Approximations of $\log2$ and Other Logarithms

We describe a new approach to estimating $\mu(\log 2)$, without improving Rukhadze's result (1987). We find estimates for approximations to the number $\log 2$ by numbers from the field $\mathbb Q(\sqrt{2})$, to the number $\log((\sqrt{5}-1)/2)$ by numbers from the field $\mathbb Q(\sqrt{5})$, and to some other numbers.