Napierian logarithm
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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
.
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