# Natural Logarithms (Log_{e} or *ln*)

Natural logarithms (also called Napierian logarithms) are logarithms to the base 'e'.
One of their main applications in biochemistry is in calculations
involving the equilibrium constants of reactions.

The value of e, to five decimal places, is 2.71828.

It is derived by evaluating as many terms in the
infinite exponential series as necessary.

Tables of *ln* are available, and are
used as in the following table:

Number | Factors | look up | add values | Answer |

8.765 | 8.765 x 10^{0} | ln 8.765 + ln 0 | 2.1708 + 0 | 2.1708 |

876.5 | 8.765 x 10^{2} | ln 8.765 + ln 10 + ln 10 | 2.1708 + 4.6052 | 6.7760 |

0.8765 | 8.765 x 10^{-1} | ln 8.765 - ln 10 | 2.1708 - 2.3026 | -0.1318 |

0.008765 | 8.765 x 10^{-3} | ln 8.765 -3 x (ln 10) | 2.1708 - 6.9078 | -4.7370 |

Note that unlike the common logarithms, natural logs have no characteristic and mantissa, thus:

- negative values are properly preceded by a negative symbol
- there is a true decimal point
- numbers at the bottom of the 'antiln'
table are in the 10
^{5} range.

##
Note that ln(x) = 2.303 log_{10}(x).

Last modified 7 April, 1996, Andrew Pearson.