The ehupfumi pamusoro logarithms, kana zvinoshamisa - pedyo ...

Kudiwa kadambari akaonekwa munhu pakarepo, achangogara akakwanisa uwandu zvinhu zvakamupoteredza. Zvinogona vaifungidzira kuti quantitative Kukoshesa pfungwa zvishoma nezvishoma kwakakonzera "wedzera-bvisa" kudiwa mhando kukarukureta. Izvi zviviri matanho ari nyore zviri kiyi pakutanga - dzimwe manipulations zvose nenhamba kuzivikanwa chokuwanziridza, nokupesana, Exponentiation , etc. - nyore "Mechanisation" zvimwe computational algorithms, izvo kwakavakirwa nyore svomhu - "peta-bvisa". Chero zvakanga, asi kusikwa algorithms kuti kadambari chikuru kubudirira mupfungwa, uye vanyori vavo achasiya nokusingaperi chiratidzo ravo kuyeuka vanhu.

Matanhatu kana manomwe emakore akapfuura mumunda mugungwa kufamba uye kudzidza nezvenyeredzi yakawedzera kudiwa yakawanda Masvomhu, izvo hazvishamisi, sezvo inozivikanwa kuMiddle Ages kukura wekushandisa uye zvenyeredzi. Maererano okuti "kwokudiwa dzinoita wedzerai" mathematicians akawanda akanga pfungwa - yokutsiva zvikuru basa-ndichibvunza nokushanda vachiwedzera maviri nhamba iri nyore kuwedzera (dually vaiona pfungwa kutsiva weboka kubudikidza kubvisa). The kushanda shanduro itsva kadambari hurongwa yakataurwa muna 1614 basa Dzhona Nepera zvinoshamisa chaizvo zita "Description of chinoshamisa patafura logarithms." Chokwadi, humwe kuvandudzika wenyika itsva vakapfuurira mberi, asi dzinokosha ehupfumi pakati logarithms vakanga mimwe Napier. Pfungwa pakuverenga maitiro achishandisa logarithms aiva kuti kana dzakatevedzana nhamba anoumba munhu geometric kunoita, logarithms avo kuumba kunoita, asi svomhu. In pamberi pre-akagadzirirwa matafura nzira itsva kugarwa nyore kuti Masvomhu, uye wokutanga yemasiraidhi mutemo (1620 gore) raiva zvichida kutanga yekare uye zvikuru vakarongeka karukureta - chinokosha ouinjiniya chokushandisa.

Nokuti kupayona munzira dzose yakazara nemakomba. Pakutanga, logarithm zvitsigiro yatorwa zvinobudirira uye dzemaitirwe kururama kwakanga pasi, asi kare muna 1624 rakanatswa tafura ane grade chawo dzakabudiswa. The ehupfumi pamusoro logarithms zvinobviswa chezvematongerwe Pakusarudza: logarithm reruoko - C number iyo, kana ukuru logarithm hwaro (nhamba A), zvichiguma zvinoverengeka b. Classic kutsikisa Ipfungwa sokunge: logA (b) = C - kuti verenga sezvinotevera: b logarithm, kuti nechigadziko A, inhamba C. Kuti aite chiito kushandisa kwete zvakajairika, theorem nhamba, unofanira kuziva mitemo, rinozivikanwa "ehupfumi logarithms. " In Zvinotaurwa, mitemo zvose zvacho zvakafanana subtext - sei kuwedzera, bvisa uye kutendeuka logarithms. Zvino tinoziva sei kuzviita.

Theorem razero uye mumwe

1. logA (1) = 0, ari logarithm nhamba 1 akaenzana 0 chero chikonzero - zvakonzerwa nhamba vamutsirwe razero dhigirii.

2. logA (A) = 1, zvakafanana logarithm pamwe chawo nhamba 1 - chiri kuzivikanwa wechokwadi chero nhamba simba rokutanga.

Kuwedzera uye kubvisa pamusoro logarithms

3. logA (m) + logA (n) = logA (m * n) - Verengai logarithms ndiyo logarithm anoverengeka kwazvo basa.

4. logA (m) - logA (n) = logA (m / n) - musiyano pakati logarithms ari nhamba, rakafanana yaimbovapo, akaenzana logarithm pakati nhamba nhamba idzi.

5. logA (1 / n) = - logA (n), kuti logarithm pamusoro Ivan Kuchin pamusoro logarithm panhamba iyi yakaenzana "kubvisa". Zviri nyore kuona kuti ichi ndicho mugumisiro yapfuura okuti 4 kuti mamita = 1.

Zviri nyore kuona kuti mitemo zvinoda 3-5 kumativi maviri chete nerogi chawo.

The exponents mu theorem mashoko

6. logA (MN) = N * logA (m), kuti logarithm mukuwanda dhigirii N akaenzana logarithm panhamba ichi, vawanda nokuda exponent n.

7. nerogi (Mab) (b) = (1 / c) * logA (b), achiverengwa se "logarithm reruoko, kana muzasi ane chimiro Ac, akaenzana zvibereko logarithm pamwe chawo B vanoverengeka neizvi C».

Formula anoshandura logarithm garo

8. logA (b) = - logC (b) / logc (A), logarithm reruoko kuna muzasi A panguva yezwi pechingoro C rinowanikwa sezvo quotient ari logarithm pamwe chawo b č uye C ari logarithm pamwe chawo nhamba yakaenzana yapfuura nechigadziko A, sezvamakaropafadzwa pamwe chiratidzo "kubvisa".

The pamusoro logarithms avo zvivako anobvumira yakakodzera chikumbiro kurerutsa dzemaitirwe huru Numeric arrays, nokudaro kuderedza nguva nhamba Masvomhu uye anopa zvinogamuchirwa kururama.

Hazvishamisi kuti zvesayenzi uye ouinjiniya zvivako zviri logarithms inoshandiswa zvoga kumiririrwa chaiko mananara. Somuenzaniso, kuzivikanwa kushandisa hama tsika - decibels kana akayera ruzha zvakanyanya uye chiedza muna wefizikisi, Mhedziso kukura nezvenyeredzi mu ph mune kemisitiri uye nevamwe.

Efficacy theorem computation tarisa nyore kana kutora, somuenzaniso, uye kuwanda shanu-digit nhamba 3 "manually" (mu wechikamu), achishandisa mabwendefa logarithms pamusoro papepa uye ondomoka utongi. Zvakakwana kutaura kuti ekupedzisira nyaya, dzemaitirwe achatora pamusoro simba mumasekonzi 10 Chii chinonyanya kushamisa ndechokuti mune ano karukureta Masvomhu aya kutora nguva, kwete zvishoma.