An essay on irrationality measures of pi and other logarithms
  We present a brief survey of the methods used in deducing upper estimates for irrationality measures of the logarithm values. We particularly expose the best known estimates for $\log2$ (due to E. Rukhadze), $\pi$ (due to M. Hata) and $\log3$ (due to G. Rhin). 
Wadim Zudilin (Moscow)