| 31. | Graph of the natural logarithm function.
|
| 32. | For example, the natural logarithm of 1.01 is 0.01 to an accuracy better than 5 parts per thousand.
|
| 33. | A similarly simple transformation can be used if the common logarithm should be exchanged by the natural logarithm.
|
| 34. | The surface area formula above gives a lower bound for the area as 2 times the natural logarithm of.
|
| 35. | The first such distribution found is } }, where is the prime-counting function and is the natural logarithm of.
|
| 36. | Since the difference between two natural logarithms is a dimensionless ratio, the trait may be measured in any unit.
|
| 37. | Then the natural logarithm could be recognized as the inverse function to the transcendental function e " x ".
|
| 38. | These properties can be manipulated after the taking of natural logarithms on both sides and before the preliminary differentiation.
|
| 39. | For instance, the binary logarithm is the natural logarithm divided by ln ( 2 ), the natural logarithm of 2.
|
| 40. | Where \ ln & thinsp; \ Gamma ( n ) denotes the natural logarithm of the gamma function at n.
|
