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...[[Addition|sum]] and [[Subtraction|difference]] of a pair of values whose logarithms are known, without knowing the values themselves.<ref name="Theodora"/> ...s <math>s_b(z)</math> and <math>d_b(z)</math> are also known as ''Gaussian logarithms''. ...

...ulus]], '''logarithmic differentiation''' or '''differentiation by taking logarithms''' is a method used to [[derivative|differentiate]] [[function (mathematics ...ic differentiation relies on the [[chain rule]] as well as properties of [[logarithms]] (in particular, the [[natural logarithm]], or the logarithm to the base ' ...

{{short description|Approximate identity involving logarithms of primes}}In [[number theory]], '''Selberg's identity''' is an approximate ...

...he algorithm gets its security from the difficulty of computing [[discrete logarithms]].<ref name="schneier">Bruce Schneier, ''Applied Cryptography: Protocols, A ...number <math>p</math> needs to be large enough so that computing discrete logarithms modulo <math>p</math> is infeasible.<ref name="schneier"/> To be more prec ...

...operation. The log semiring also arises when working with numbers that are logarithms (measured on a [[logarithmic scale]]), such as [[decibel]]s (see {{slink|De ...n is the same as usual addition, <math>x \otimes_b y = x + y</math>, since logarithms take multiplication to addition; however, log addition depends on base. The ...

...may be seen as a generalisation of [[Baker's theorem]] on linear forms in logarithms. [[Gisbert Wüstholz]] proved it in the 1980s.<ref>{{cite journal | last=Wüs ...cceeded to get the final expected form for lower bound for linear forms in logarithms. This was put into an effective form in a joint work of him with [[Alan Bak ...

...adleman">L. Adleman, M.D. Huang. "Function Field Sieve Method for Discrete Logarithms over Finite Fields". In: Inf. Comput. 151 (May 1999), pp. 5-16. DOI: 10.100 ...f D. Coppersmith <ref>D. Coppersmith. (1984), "Fast evaluation of discrete logarithms in fields of characteristic two". In: IEEE Trans. Inform. Theory IT-39 (198 ...

...theory, [[Transcendental number theory|transcendence]], [[linear forms in logarithms]], [[Effective results in number theory|effective methods]], [[Diophantine *{{Citation | last1=Baker | first1=Alan | title=Linear forms in the logarithms of algebraic numbers. I | doi=10.1112/S0025579300003971 | mr=0220680 | year ...

...hematics)|regulator]] defined using p-adic logarithms instead of the usual logarithms, introduced by {{harvs|txt|authorlink=Heinrich-Wolfgang Leopoldt|first=H.-W ...

...rtin|last2=Ruf|first2=Johannes|date=2019|title=Stochastic exponentials and logarithms on stochastic intervals — A survey|journal=Journal of Mathematical Analysis ...rtin|last2=Ruf|first2=Johannes|date=2019|title=Stochastic exponentials and logarithms on stochastic intervals — A survey|journal=Journal of Mathematical Analysis ...

{{short description|On algebraic independence of logarithms}} To simplify notation, let <math>\mathbb{L}</math> be the set of logarithms to the base ''e'' of nonzero [[algebraic number]]s, that is ...

==Bootstrapping other logarithms== ...tabulate the logarithms of the [[prime number]]s and in the next layer the logarithms of the [[Composite number|composite]] numbers {{math|''c''}} based on their ...

If [[binary logarithm|base 2 logarithms]] and powers of 2 are used instead, then the unit of information is the [[s ...

...(q) = e^{\sqrt{\ln q \times \ln\ln q}}</math> though after that individual logarithms can be calculated fairly quickly."</ref> It turns out that much Internet tr ...e data for a single 512-bit prime. Once that was done, however, individual logarithms could be solved in about a minute using two 18-core [[Intel Xeon]] CPUs.<re ...

...'dman|first=N I|date=1968|title=Improved Estimate For A Linear Form Of The Logarithms Of Algebraic Numbers|journal=Mathematics of the USSR-Sbornik|volume=6|issue ...

...ator]] and [[denominator]] are equal. Other ratios are compared to one by logarithms, often [[common logarithm]] using base 10. The ratio scale then segments by ...the [[additive identity]]), known as the [[probability semiring]]; taking logarithms (with a choice of base giving a [[logarithmic unit]]) gives an [[isomorphis ...

...a sequence of exponentiations of terms of an arithmetic sequence. Sums of logarithms correspond to products of exponentiated values. ...

[[Category:Logarithms]] ...

...uary 2022|reason=it doesn't describe what the current records for discrete logarithms are.}} ...u/cgi-bin/wa.exe?A2=NMBRTHRY;fd743373.1912 “795-bit factoring and discrete logarithms,”] December 2, 2019.</ref><ref>F. Boudot et al, [https://eprint.iacr.org/20 ...

===Exponential and logarithms=== ...