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pl_terranine

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- Thread starter pl_terranine
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pl_terranine

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lurflurf

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From a modern prospective we want logs to have this propertypl_terranine said:

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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jma2001

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pl_terranine said:

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pl_terranine

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thank you jma i'll check out that book.

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