Definition:Napierian Logarithm

Definition

The Napierian logarithms are a system of logarithms where:

$\log_{\text {Nap} } 10 \, 000 \, 000 = 0$

$\log_{\text {Nap} } 9 \, 999 \, 999 = 1$

Thus:

$\log_{\text {Nap} } 10^7 x y = \log_{\text {Nap} } x + \log_{\text{Nap} } y$

Also defined as

Many sources use the term Napierian logarithm for natural (base $e$) logarithms.

It is wise to make sure of which is meant when referring to them.

Also see

• Results about Napierian logarithms can be found here.

Source of Name

This entry was named for John Napier.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Napierian logarithm: 1.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Napier, John (1550-1617)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Napier, John (1550-1617)
• 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $5$: Eternal Triangles: Napierian logarithms
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Napier, John (1550-1617)
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Napier, John (1550-1617)