Logarithms with other bases than e

DEFINITION
Logarithms are defined in terms of a real number A>1, which is called the base of the logarithms. For any number X>0 we define LOGA(X)=Y where Y is the real number such that A**Y=X.

ALGORITHM
For given A and X is LOGA(X)=LN(X)/LN(A) where the LN function is natural logarithm. The most useful numbers for us in this connection are LN(2) and LN(10). There are two simple function returning first 200 decimal digits of these constants. For their computation I used an algorithm from Natural logarithm, see the LN2P function. And the program for automatic creating a function from value of constant, see Technique: Beforehand computed constants.  

LN2: procedure; V = '' V = V || 0.69314718055994530941723212145817656807
V = V || 5500134360255254120680009493393621969694
V = V || 7156058633269964186875420014810205706857
V = V || 3368552023575813055703267075163507596193
V = V || 0727570828371435190307038623891673471123350
return V

 

LN10: procedure; V = ''
V = V || 2.30258509299404568401799145468436420760
V = V || 1101488628772976033327900967572609677352
V = V || 4802359972050895982983419677840422862486
V = V || 3340952546508280675666628736909878168948
V = V || 2907208325554680843799894826233198528393505
return V

 

CONNECTIONS


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last modified 1st August 2001
Copyright 2000-2001 Vladimir Zabrodsky
Czech Republic