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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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/

[1] Rukhadze E. A., “Otsenka snizu priblizheniya $\ln2$ ratsionalnymi chislami”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 1987, no. 6, 25–29 | MR | Zbl

[2] Salikhov V. Kh., “O mere irratsionalnosti $\log3$”, Dokl. RAN, 417:6 (2007), 753–755 | MR | Zbl

[3] Salnikova E. S., “Diofantovy priblizheniya $\log2$ i drugikh logarifmov”, Mat. zametki, 83:3 (2008), 428–438 | DOI | MR | Zbl

[4] Salnikova E. S., “Priblizheniya nekotorykh logarifmov chislami iz polei $\mathbb Q$ i $\mathbb Q(\sqrt d)$”, Fundament. i prikl. mat., 16:6 (2010), 139–155 | MR

[5] Tomashevskaya E. B., “Sovmestnoe priblizhenie $\log2$ i $\operatorname{arctg}\frac17$”, Vestnik BGTU, 2006, no. 4, 126–130

[6] Amoroso F., Viola C., “Approximation measures for logarithms of algebraic numbers”, Ann. Scu. Norm. Sup. Pisa Cl. Sci., 30 (2001), 225–249 | MR | Zbl

[7] Hata M., “Rational approximations to $\pi$ and some other numbers”, Acta Arith., 63:4 (1993), 335–349 | MR | Zbl

[8] Heimonen A., Matala-aho T., Väänänen K., “On irrationality measures of the values of Gauss hypergeometric function”, Manuscripta Math., 81:1 (1993), 183–202 | DOI | MR | Zbl