the.com/natural logarithm
The logarithm nature actually uses, because e shows up everywhere growth happens.
means The logarithm with base e (≈2.71828), written ln(x), that tells you how long something must grow continuously at its own rate to reach a given size.
from 'Logarithm' comes from Greek logos (ratio/proportion) plus arithmos (number), coined by John Napier in the early 1600s as 'logarithmus.' The 'natural' part arrived once mathematicians realized one particular base — e, discovered through compound-interest problems and formalized by Euler in the 1700s — kept appearing on its own in calculus and growth equations, without anyone having to choose it. So this logarithm earned the name 'natural' simply because, unlike base 10 or base 2, nobody picked it; it picked itself.
- written as
- ln(x), not log(x)
- base
- e, approximately 2.71828
- shows up in
- compound interest, decay, entropy, primes
- derivative
- 1/x, cleanest slope in calculus