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Napierian Logarithm

\begin{figure}\begin{center}\BoxedEPSF{NapierianLogarithm.epsf}\end{center}\end{figure}

Write a number $N$ as

\begin{displaymath}
N=10^7(1-10^{-7})^L,
\end{displaymath}

then $L$ is the Napierian logarithm of $N$. This was the original definition of a Logarithm, and can be given in terms of the modern Logarithm as

\begin{displaymath}
L(N)=-{\log\left({n\over 10^7}\right)\over\log\left({10^7\over 10^7-1}\right)}.
\end{displaymath}

The Napierian logarithm decreases with increasing numbers and does not satisfy many of the fundamental properties of the modern Logarithm, e.g.,

\begin{displaymath}
\mathop{\rm Nlog}\nolimits(xy)\not=\mathop{\rm Nlog}\nolimits x+\mathop{\rm Nlog}\nolimits y.
\end{displaymath}




© 1996-9 Eric W. Weisstein
1999-05-25