# The history of logarithms

pl_terranine
is anyone able to recommend a book or a site for a high school senior that explains how logarithmic tables are made and its connection to ln/e.

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pl_terranine said:
is anyone able to recommend a book or a site for a high school senior that explains how logarithmic tables are made and its connection to ln/e.
From a modern prospective we want logs to have this property
log(x)+log(y)=log(xy)
for all x,y and for the function to be a bijection (1-1 and onto)
This is called an isomorphism. It allows us to do multiplication in terms of addition. This desired property does not define a function as many functions have this property. Thus we also require log(b)=1 for some number b called the base. When logarithums were invented modern prospective was not availiable so the functions napier defined were not as nice
NapLog(N)=log(N/10^7)/log(10^7-1)
in modern notation.
The first log tables we calculated doing multiplications with prime numbers and noting that the NapLog if ploted has
NapLog(10^7)=0 and 1/slope=N*Naplog(10^7-1)
As logs got popular later tables used more convienent bases like e (natural log) and 10 (common log). Calculation of log tables then used more and more methods from calculus. Later computers were used to calculate tables. Now calculators and computers have largely made tables obsolete.
see this site
http://mathworld.wolfram.com/NapierianLogarithm.html

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pl_terranine said:
is anyone able to recommend a book or a site for a high school senior that explains how logarithmic tables are made and its connection to ln/e.
e: The Story of a Number by Eli Maor. I read it last year and it covers exactly the information you are looking for.

pl_terranine
thank you jma i'll check out that book.