41. Variations of this argument can be used to produce continued fraction expansions for the natural logarithm , the generalized binomial series. 42. For instance, the binary logarithm is the natural logarithm divided by ln ( 2 ), the natural logarithm of 2. 43. Here,'log'denotes the natural logarithm . 44. Where x _ 1 and x _ 2 are the values of interest ( amplitudes ), and is the natural logarithm . 45. This is based on the natural logarithm of the number of macrostate ( W or ? ) called the thermodynamic probability. 46. The double natural logarithm ( ln ln ) indicates that the divergence might be very slow, which is indeed the case. 47. In contrast, also shown is a picture of the natural logarithm function and some of its Taylor polynomials around 0 } }. 48. At that specific point the " slope " of the curve of the graph of the natural logarithm is also precisely one. 49. Leonhard Euler introduced the letter as the base for natural logarithms , writing in a letter to Christian Goldbach of 25 November 1731. 50. The diagram itself is a plot of the natural logarithm of the volume or yield against the natural logarithm of stems per acre.
