Logarithms with other bases than e
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.
For given A
where the LN
function is natural logarithm
. The most useful numbers for us in this connection are LN(2)
. 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
LN10: procedure; V = ''
V = V || 2.30258509299404568401799145468436420760
V = V || 1101488628772976033327900967572609677352
V = V || 4802359972050895982983419677840422862486
V = V || 3340952546508280675666628736909878168948
V = V || 2907208325554680843799894826233198528393505
last modified 8th August 2001
Copyright © 2000-2001 Vladimir Zabrodsky