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The Napierian logarithm, as first defined by John Napier , is a function which can be defined in terms of the modern logarithm by:
A plot of the Napierian logarithm for values between 0 and 10.
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{\displaystyle \mathrm {NapLog} (x)={\frac {\log {\frac {10^{7}}{x}}}{\log {\frac {10^{7}}{10^{7}-1}}}}.}
(Being a quotient of logarithms, the base of the logarithm chosen is irrelevant.)
It is not a logarithm to any particular base in the modern sense of the term, however, it can be rewritten as:
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{\displaystyle \mathrm {NapLog} (x)=\log _{\frac {10^{7}}{10^{7}-1}}10^{7}-\log _{\frac {10^{7}}{10^{7}-1}}x.}
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