# Natural Logarithms (Loge 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 100 ln 8.765 + ln 0 2.1708 + 0 2.1708 876.5 8.765 x 102 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 105 range.