Napierian Logarithm

Author

Eric W. Weisstein
November 23, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/NapierianLogarithm.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/NapierianLogarithm.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Equations

Solve[10^7(1-10^(-7))^L==n,L]

FullSimplify[%,n>0]

NLog[n_]:=(Log[n]-Log[10^7])/(Log[10^7-1]-Log[10^7])

Simplify[NLog[n]]

Identities

NapLog[n_]:=((Log[(10000000/n)])/(Log[(10000000/9999999)]))

Simplify[Subtract@@{NapLog[Sqrt[N1 N2]],(NapLog[N1]+NapLog[N2])/2},N1>0&&N2>0]

Simplify[Subtract@@{NapLog[10^-7 N1 N2],NapLog[N1]+NapLog[N2]},N1>0&&N2>0]

Simplify[Subtract@@{NapLog[10^7 N1/N2],NapLog[N1]-NapLog[N2]},N1>0&&N2>0]

Plot

Plot[NLog[n],{n,.001,1},PlotStyle->Red,AxesLabel->{x,NapLog[x]}]