Napierian logarithm

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Definition
  1. Noun:
    • A logarithm to the base e: A Napierian logarithm is a specific type of logarithm where the base is the mathematical constant e (approximately 2.71828). It is the inverse function to the exponential function with base e.
Usage
  • The term "Napierian logarithm" is used in mathematics, particularly in historical contexts or specific fields like calculus, to refer to the natural logarithm. It is synonymous with "natural logarithm."
  • It is named after John Napier, a Scottish mathematician who invented logarithms.
Examples
  • Noun:
    • The equation requires you to take the Napierian logarithm of both sides.
    • Early mathematical tables listed Napierian logarithms for various numbers.
Advanced Usage
  • Historical Context: While "natural logarithm" is the more common modern term, "Napierian logarithm" acknowledges the historical origin. In some older texts or specific technical discussions, this term may still be used.
  • Mathematical Notation: The Napierian logarithm of a number is written as ln() or sometimes logₑ().
Variants and Related Words
  • Natural logarithm (n): The modern, more common term for a logarithm to the base .
    • The derivative of the natural logarithm of x is 1/x.
  • Logarithm (n): The general mathematical operation of which the Napierian logarithm is a specific type.
  • Exponential function (n): The function , which is the inverse of the Napierian logarithm.
Synonyms
  • Natural logarithm: The direct and most common synonym.
  • Log to the base e: A descriptive synonym.
Related Phrases
  • Common logarithm: This phrase contrasts with "Napierian logarithm," as it refers to a logarithm to the base 10 (log₁₀).
  • Change of base: A formula that allows conversion between logarithms of different bases, such as converting a Napierian logarithm to a common logarithm.
Noun
  1. a logarithm to the base e

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