Napierian logarithm


The term Napierian logarithm or Naperian logarithm, named after John Napier, is often used to mean the natural logarithm. Napier did not introduce this natural logarithmic function, although it is named after him. However, if it is taken to mean the "logarithms" as originally produced by Napier, it is a function given by :
The Napierian logarithm satisfies identities quite similar to the modern logarithm, such as
or

Properties

Napier's "logarithm" is related to the natural logarithm by the relation
and to the common logarithm by
Note that
and
Napierian logarithms are essentially natural logarithms with decimal points shifted 7 places rightward and with sign reversed. For instance the logarithmic values
would have the corresponding Napierian logarithms:
For further detail, see history of logarithms.