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Natural Logarithm Overview
en.wikipedia.org/wiki/Natural_logarithmYapay zekadan makale özeti
- Definition and Notation
- Natural logarithm is logarithm to base e, approximately 2.718281828459
- Written as ln x, loge x, or simply log x
- Natural logarithm of e is 1, natural logarithm of 1 is 0
- Mathematical Properties
- Inverse function of exponential function
- Area under curve y = 1/x between 1 and a
- Derivative exists for positive real numbers
- Taylor series converges for x > 1
- Computational Aspects
- Taylor series approach inefficient for large x values
- Halley's or Newton's methods provide faster convergence
- Special log1p function available for accurate near-zero calculations
- Complex logarithm exists only on cut plane
- Historical Development
- Concept worked out by Saint-Vincent and Sarasa before 1649
- First mentioned by Mercator in 1668
- John Speidell compiled effective natural logarithms in 1619