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