LOGARIFMi adadi N

LOGARIFMi adadi N az rui asosii, nishondihandai darajai m, ki baroi hosil kardani N adadi a (asosi Logarifm)-ro t marotiba darajabardori kardan lozim ast; ishoratash loga/V. Hamin tavr, agar anN boshad, t» = lo BaN ast. Mas., logfll = 0, logiolOOO — 3, log|243 * 5, zero a0 — =» 1, 103 = 1000, 3s – 243 meboshad. Hangomi a<0 budan, beintiho bisyor adadhoi musbat Logarifm nadorand, binobar in a>0 va af 1 megirand. Az khosiyathoi funksiyai logarifmi barmeoyad, ki dar gula adadi musbat az rui asosi dodashuda tanho yakto Logarifm dorad (Logarifmi adadi manfi adadi kompleksi ast). Khosiyathoi asosii Logarifm:

Agar asosi Logarifm a = 10 boshad, Logarifmro dahi menomand va bo IgiV ishora mekunand. Logarifmi dahii N, kn az Yu (k — adadi butun) farq mekunad, adadi transseidenti meboshad va az in sabab qimathoi Logarifmi adadho dar jadvali Logarifmho ba vositai kasri dahii okhirnok taqribi doda meshavand. Qismi kasrii Logarifmi dahii adadi N mantissa va qismi butunash kharakteristikai in Logarifm nomida meshavad. Mas., kharakternstikai lg 20= = 1.3010 ba 1 va mantissaash ba 0,3010 barobar ast. Logarifmi dahii adadhoi az 1 kalon musbat (lgl = 0) va adadhoi az 1 khurd manfi meboshad. Agar Logarifm manfi boshad, mantissai onro musbat va kharakteristikaashro manfi navishtan ba maqsad muvofiq ast. Mas., lg 0,2 «= lg 2 — lg 10 » = 0,30103 — 1 yo lg 0,2 = 1,69897.

Dar tadqiqoti nazariyavi Logarifmhoe, ki asosashon ba adadi e == 2,71828… barobar meboshad, ahamiyati kalon dorand. In guna Logarifmro logarifmi naturali menomand va in tavr ishorat mekunand: In N. Baroi Logarifmi adadi N-ro az rui asosi a bo Logarifmi zamon adad az rui asosi 6 ivaz namudan formulai zerinro istifoda mebarand:

Dar in formula zarbshavandai t/logab-po moduli guzarishi Logarifmi asosash a ba L.-i asosash 6 menomand.

 Ad.: Istoriya matematiki, t. 2, M., 1070.       M. Ismatov,