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 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).

Created and maintained by Andrew Pearson and Robert Lancashire,
University of the West Indies, Mona Campus, Jamaica.
Comments to authors at Andrew Pearson and/or Robert Lancashire.
Created Monday Apr 15th 1996. Last modified Wednesday May 15th 1996.

Natural Logarithms (Loge or ln)

Note that ln(x) = 2.303 log10(x).

Natural Logarithms (Log_e or ln)

Note that ln(x) = 2.303 log₁₀(x).