Revision as of 21:10, 29 November 2007 editCgibbard (talk | contribs)97 editsNo edit summary← Previous edit | Revision as of 12:09, 11 March 2008 edit undoEric Kvaalen (talk | contribs)Extended confirmed users10,284 edits Use in meaning natural logarithm. Additional expression, in terms of ln.Next edit → | ||
Line 1: | Line 1: | ||
The Napierian logarithm, as first defined by ], is a function which can be defined in terms of the modern ] by: | The term Napierian logarithm, or Naperian logarithm, is often used to mean the ], but as first defined by ], it is a function which can be defined in terms of the modern ] by: | ||
] | ] | ||
Line 12: | Line 12: | ||
and hence it is a linear function of a particular logarithm, and so satisfies identities quite similar to the modern one. | and hence it is a linear function of a particular logarithm, and so satisfies identities quite similar to the modern one. | ||
The Napierian logarithm is related to the ] by the relation | |||
<math>\mathrm{NapLog} (x) \approx 9999999.5 (16.11809565 - \ln(x))</math> | |||
and to the ] by | |||
<math>\mathrm{NapLog} (x) \approx 23025850 (7 - \log_{10}(x))</math>. | |||
Revision as of 12:09, 11 March 2008
The term Napierian logarithm, or Naperian logarithm, is often used to mean the natural logarithm, but as first defined by John Napier, it is a function which can be defined in terms of the modern logarithm by:
(Being a quotient of logarithms, the base of the logarithm chosen is irrelevant.)
It is not a logarithm to any particular base in the modern sense of the term, however, it can be rewritten as:
and hence it is a linear function of a particular logarithm, and so satisfies identities quite similar to the modern one.
The Napierian logarithm is related to the natural logarithm by the relation
and to the common logarithm by
.
This mathematics-related article is a stub. You can help Misplaced Pages by expanding it. |