Geodesic
On Diophantine approximations to~$\log x$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 6, pp. 157-166

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A lower bound for Diophantine approximations to linear combination of the numbers $\log(5/3)$ and $(1/\sqrt{15})\operatorname{arctan}(1/\sqrt{15})$ is obtained. 
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     author = {E. B. Tomashevskaya},
     title = {On {Diophantine} approximations to~$\log x$},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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     publisher = {mathdoc},
     volume = {16},
     number = {6},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2010_16_6_a11/}
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E. B. Tomashevskaya. On Diophantine approximations to~$\log x$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 6, pp. 157-166. http://geodesic.mathdoc.fr/item/FPM_2010_16_6_a11/