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: