Waa maxay logarithm ah?

Qarniyadii dhexe oo loo yaqaan waqtiga safarka iyo juquraafi helay. Habka keliya ee lagu xaqiijin lahaa safarka long-distance ahaa shiraaca in had iyo jeer la xidhiidha hirgelinta tiro badan xisaabinta navigation. Way adag tahay in la damacsan habka of maaanka xisaabaha in dhufasho, kala qeybinta tirooyinka shan god "by gacanta". Dzhon Neper, fiqi ah by nooca ganacsiga ay muhiimka ah, ku hawlan firaaqada ah xisaabinta trigonometric sarcaadka bedelo nidaamka caadi ah ee isku dhufashada by sii dheer fudud. isaga qudhiisuse wuxuu ku sheegay in uu ahaa goolkiisii ahayd in "laga takhaluso oo ka mid ah dhib iyo tedium xisaabinta, kaas oo lagu daciifiyay badan ka daraasadda xisaabta." Dadaalka ay ku guulaystaan - qalab xisaabeed loo yaqaan nidaamka logarithms waxaa la abuuray.

Waa maxay logarithm ah? The salaysan xisaabinta ku logardam waa wakiil kale ee: halkii nidaamka meelaynta caadiga ah, sida aan loo isticmaalo, tirada A waxaa wakiil sida xoogga ah ee ra'yi dhiibashada, halkaas oo qaar ka mid ah tirada loo aabo yeelin N, loo yaqaan dhibic saldhig la sara kiciyaa si n degree ah, in natiijadu waa tiro A. ahu wuxuu , n - waa logarithm si N. saldhig doorashada A of radikis qoran magaca nidaamka. Waayo, logarithms jajab tobanle sahlan vichisleny codsatay nidaamka, iyo sayniska iyo teknolojiga hubkaas ayaa loo isticmaalaa nidaamka dabiiciga ah ee logarithms, kuna waari dhexdeeda ee saldhiga ah waa ah e tiro aan buuxin = 2,718. Tibaaxda qeexaya logarithm ee tirada A, Afka xisaabta waxaa ku qoran sida soo socota:

n = log (N) A, halkaas oo N - degree saldhig.

logarithms tobanle iyo dabiiciga ah waxay leeyihiin qoraal ah loo soo gaabiyo gaar ah - LGA iyo lnA, siday u kala horreeyaan.

xisaabaha Nidaamka isticmaalaya logarithms ee xisaabinta, element ugu weyn waa beddelidda ee tirada qaab awood ah oo ay logarithms of miiska saldhig qaar ka mid ah, tusaale ahaan 10. khalkhalgelinta Tani waa mid sahlan. Next, isticmaalaan awood hantida lambarada, oo ka kooban in xaqiiqda ah in marka heerka uu xeradooduna waxay sii badisay. In tababar, taas macnaheedu waa in isku dhufashada tirooyinka la matalaad logardam ah waxaa lagu bedelaa ku daray awoodooda. Sidaa darteed, su'aasha "Waa maxay logarithm ah" haddii ay tahay in ay sii wadaan in ay "iyo sababta aan u baahan tahay," waa jawaabta fudud - si loo fududeeyo habka for the dhufashada-qaybinta tirooyin godad badan - waayo waxaa dheer "khaanadda a" waa fududdahay in lagu dhufto "khaanadda a". Yaa ma rumaysan - ha isku dayaan in ay iska jiifsaday iyo in lagu dhufto laba tiro oo sideed-bit.

Shaxda koowaad ee logarithms (saldhigyo ku leh dhowr ah oo dabiici ah), lagu daabacay 1614 Dzhon Neper, oo gebi ahaanba bilaash ah qaladaad doorasho iyo ay ka mid yihiin miis ka logarithms caadi ah, u muuqday in 1857 iyo waxaa loo yaqaan miiska Bremikera. Isticmaalka logarithms saldhig ee foomka of tiro aan buuxin sababtoo ah tirada waa, arrin si fudud u helay iyada oo loo marayo taxanaha Taylor isagoo codsiga ballaaran in lagama maarmaan iyo kalkulaska kala duwan.

Nuxurka nidaamka computer this siisaa jawaab su'aasha "Waa maxay logarithm" iyo waxaa soo socota ka aqoonsi logardam ah oo aasaasi ah: N (saldhig logarithm) sara kiciyey si ay xoogga n, si siman u logarithm ee tirada A (logą), tirada this waa loo siman yahay si A. Xaaladdan oo kale, A> 0, ie logarithm waxaa ka go'an oo kaliya tirooyinka togan, oo saldhig log ee had iyo jeer waa ka weyn yahay 0 oo aan si siman u 1. Iyada oo ku saleysan ku qorani, sifooyinka logarithm dabiiciga ah loo diyaariyey laga yaabaa in sida soo socota:

1. Field of logarithm dabiiciga ah - oo dhan dhidibka tiro ka bilaabmaysa 0 ilaa xad.
2. lihida x = 0 - natiijo ah oo xiriir ah oo loo yaqaan - tiro ka mid ah eber degree waa 1.
3. lihida (* Y X) = lihida X + lnY - ugu muhiimsan ee hantida khalkhalgelinta xisaabeed - logarithm ee alaabta laba tiro oo ramen wadarta ah logarithms ee kasta.
4. lihida (X / Y) = lihida X - lnY - logarithm ee qeybtu waxay laba tiro oo waa loo siman yahay si ay u kala duwan yihiin oo ka mid ah logarithms of lambaradan.
5. lihida (X) n = n * lihida X.
6. logarithm The dabiiciga ah waa hawl differentiable convex sii weynaydba, kuna waari dhexdeeda lihida 'X = 1 / X
7. gasho (N) A = K * lihida A - logarithm sida ay wax wanaagsan oo aan ka ahayn e saldhig ee dabiiciga ah oo kaliya ka duwan saamiga.

Haddaba walba oo dhigta dugsiga ogyahay in uu yahay logarithm ah, laakiin in horumarka berrinkii dhibaatooyinka injineernimada computer dhaqmo shaqada xisaabeed mahad tageen. Si kastaba ha ahaatee, logarithms, mar hore sidii qalab xisaabeed loo isticmaalo isla'egta la dahsoon ee jibbaarada ee ra'yi dhiibashada ee helida markii suuska of radioactive xubno ka iyo meelaha kale ee xisaabta, fisigiska iyo tirakoobka.