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 (in terms of the modern natural logarithm):

${\displaystyle \mathrm {NapLog} (x)=-10^{7}\ln(x/10^{7})}$

The Napierian logarithm satisfies identities quite similar to the modern logarithm, such as

${\displaystyle \mathrm {NapLog} (xy)\approx \mathrm {NapLog} (x)+\mathrm {NapLog} (y)-161180956}$

or

${\displaystyle \mathrm {NapLog} (xy/10^{7})=\mathrm {NapLog} (x)+\mathrm {NapLog} (y)}$

In Napier's 1614 Mirifici Logarithmorum Canonis Descriptio, he provides tables of logarithms of sines for 0 to 90°, where the values given (columns 3 and 5) are

${\displaystyle \mathrm {NapLog} (\theta )=-10^{7}\ln(\sin(\theta ))}$