The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718 281 828 459.The natural logarithm of x is generally written as ln x, log e x, or sometimes, if the base e is implicit, simply log x. Parentheses are sometimes added for clarity, giving ln(x), log e (x), or log(x).

If a bar contains a double sharp or double flat accidental and the composer wishes to denote the same note with only a single sharp or flat, a natural sign traditionally precedes the (single) sharp or flat symbol. Naturals are assumed (by default) in key signatures and mentioned only in key signature changes. The natural sign is derived from a square b used to denote B ♮ in medieval …

The natural unit of information (symbol: nat), sometimes also nit or nepit, is a unit of information, based on natural logarithms and powers of e, rather than the powers of 2 and base 2 logarithms, which define the shannon.This unit is also known by its unit symbol, the nat. One nat is the information content of an event when the probability of that event occurring is 1/e.