21. When using the natural logarithm of base \ displaystyle e, the unit will be the hartley. 22. The maximum is at x = e, where " e " denotes the base of natural logarithms . 23. The natural logarithm of is the first Chebyshev function, written or, which approaches the linear for large. 24. This observation led to the natural logarithm . 25. The book contained fifty-seven pages of explanatory matter and ninety pages of tables related to natural logarithms . 26. With e being the base of natural logarithms , and a and b being arbitrary positive real constants. 27. This formula is a special case of the Mercator series, the Taylor series for the natural logarithm . 28. E-- formally known as the base of the natural logarithm -- begins 2 . 718281828 and goes on forever. 29. If, this is equal to the exponential of the arithmetic mean of the natural logarithms of the numbers: 30. In physics and also in computation of Theil index, the natural logarithm is chosen as the logarithmic base.
