Geodesic
Diophantine Approximations of $\log2$ and Other Logarithms
Matematičeskie zametki, Tome 83 (2008) no. 3, pp. 428-438

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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.
Mots-clés : Diophantine approximation, Euler's formula, Goursat formula.
Keywords: irrationality exponent, irrationality measure, Gauss hypergeometric function, Kummer's formula 
@article{MZM_2008_83_3_a8,
     author = {E. S. Salnikova},
     title = {Diophantine {Approximations} of $\log2$ and {Other} {Logarithms}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {428--438},
     publisher = {mathdoc},
     volume = {83},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_3_a8/}
}
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E. S. Salnikova. Diophantine Approximations of $\log2$ and Other Logarithms. Matematičeskie zametki, Tome 83 (2008) no. 3, pp. 428-438. http://geodesic.mathdoc.fr/item/MZM_2008_83_3_a8/