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