Natural Logarithms (Log_e or ln)

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.

Note that ln(x) = 2.303 log₁₀(x).