The sifooyinka logarithms, ama la yaab leh - socda si ay ...

Baahida loo qabo Kombuyuutarada muuqday in qofka si degdeg ah, sida ugu dhakhsaha badan, wuxuu ahaa awoodaan in ay tiradeeda walxaha isaga ka ag dhow. Waxaa la malaysan karin in macquulka ah qiimeynta taranta si tartiib tartiib ah u horseeday inay ku baahida loo qabo nooca xisaab "dar-gooyaan". Labadan talaabooyin fudud yihiin muhiim ah marka hore - oo dhan manipulations kale oo leh tirooyinka loo yaqaan iskudhufashada, qeybinta, exponentiation , iwm - a fudud "mechanization" qaar ka mid ah algorithms xisaabeed, kaas oo ku salaysan yihiin xisaabta fudud - "laab-gooyaan". Wax kasta oo ay ahayd, laakiin abuurka algorithms for Kombuyuutarada waa guul weyn oo fikirka ah, iyo qorayaasha ay weligood ka tagi doono ay calaamaddu ku xasuusta binu-aadmiga oo.

Lix ama toddoba qarni ka hor berrinkii navigation badda iyo xiddigaha uu kordhay baahida loo qabo in tiro badan oo ah xisaabinta, taas oo aan la yaab leh, tan iyo waxaa la ogsoon yahay in qarniyadii dhexe horumarinta navigation iyo xiddigaha. In la ilaalinayo ee "sahayda eyda dalabka" erayadani dhowr xisaabyahannada lahaa fikradda ah - si uu u badalo howlgalka heer sare ah shaqada-xoogan ee dhufashada labada tiro fudud Intaa waxaa dheer (gidigood tixgeliyo fikrada ah si ay ugu bedesho horyaalka by goynta). version-shaqaynta nidaamka cusub ee Kombuyuutarada waxaa ka soo baxay in 1614 ka shaqaynayeen Dzhona Nepera la horyaalka ah oo aad u cajiib ah "Description of miiska cajiib ah oo logarithms." Dabcan, horumarinta dheeraad ah ee nidaamka cusub iyo ku tegey, laakiin sifooyinka aasaasiga ah ee logarithms ayaa ka soo baxay dheeraad ah Napier. Fikradda ah xisaabinta nidaamka la isticmaalayo logarithms ahayd in haddii taxane ah oo tirada foomamka ah horumarka joomateri, logarithms ay sidoo kale u sameeyaan a horumarka, laakiin xisaabta. In joogitaanka loox pre-qorshaynay hab cusub ee dejinta fududeeyey xisaabinta, iyo ugu horeysay ee sharci slide (1620 sano) wuxuu ahaa laga yaabaa in calculator qadiimiga ah iyo si sare hufan ugu horeysay - qalab injineernimada maarmaan.

Waayo horseedka wadada had iyo jeer la godadka. Markii hore, logarithm ee salka loo qaaday si guul iyo saxsanaanta xisaabinta ahaa hooseeyo, laakiin durba 1624 miiska la safeeyey saldhig jajab tobanle lagu daabacay. The sifooyinka logarithms yihiin oo ka soo jeeda muhiimad go'aaminta: logarithm of b - C waa tiro taas oo, marka heerka uu salka logarithm (tirada A), taasoo keentay in tiro ka mid ah b. doorasho lagu qoro Classic u eg: logą (b) = C - in ka akhriyi sida soo socota: logarithm b, inay saldhig A ah, waa tirada C. Si ay u qabtaan ficil la isticmaalayo, tirada aan caadi logardam ah, waxaad u baahan tahay in la ogaado set oo ah sharciyada, loo yaqaan "hantida logarithms. " Mabda ', oo dhan xeerarka leeyihiin hignaseyno caadi ah - sida loo dar, kala-gooyaan iyo badalo logarithms. Imminka waxaannu garanaynaa sida loo sameeyo.

eber logardam ah iyo mid

1. logą (1) = 0, logarithm ee tirada 1 waa loo siman yahay si 0 sabab kasta - natiijada tooska ah ee tiro kiciyey eber degree.

2. logą (A) = 1, logarithm isla lambarka saldhiga waa 1 - waxaa sidoo kale si fiican u yaqaan run lambarka mid ka mid ah awoodda ugu horeysay.

Isku geynta iyo kala goynta ee logarithms

3. logą (m) + logą (n) = logą (m * n) - wadarta logarithms waa logarithm ee tiro dhowr ah oo shaqo.

4. logą (m) - logą (n) = logą (m / n) - farqiga u ah logarithms oo ka mid ah lambarada, la mid ah ka mid ah la soo dhaafay, waa loo siman yahay si logarithm ee ratio of lambaradan.

5. logą (1 / n) = - logą (n), logarithm ee bedelka ah ee logarithm ee tirada this waa loo siman yahay si "jaray". Waa ay fududahay in aad aragto in ay tani tahay natiijada ah ee ra'yi dhiibashada hore 4 m = 1.

Waa ay fududahay in aad aragto in xeerarka u baahan tahay 3-5 labada dhinac ee saldhigga ah isla log.

The jibbaarka ah marka la eego logardam

6. logą (MN) = n * logą (m), logarithm ee tirada degree n waa loo siman yahay si logarithm tirada this, by n jibaaranaha ay bateen.

7. log (AC) (b) = (1 / c) * logą (b), waxaa la akhriyo sida "logarithm ee b, haddii salka uu leeyahay qaab AC, loo siman yahay si wax soo saarka ee logarithm la saldhig b iyo Tiro ka mid ah badisay c».

Formula badala saldhig logarithm

8. logą (b) = - logC (b) / logc (A), logarithm of b saldhig A ee kala guurka ah si ay saldhig C ah waxaa loo xisaabiyaa sida qeyb ka mid ah logarithm la saldhig b C iyo C logarithm la tirada salka loo siman yahay saldhigga A hore, kuna waari dhexdeeda la "jaray" calaamada.

The logarithms kor ku xusan iyo Xoolahooda inay u ogolaan codsiga ku habboon si ay u fududeeyaan xisaabinta oo ka mid ah Arrays tiro badan oo, taasoo waqti ka mid ah xisaabaha tiro iyo bixisaa sax aqbali karo.

Ma aha la yaab leh in in guryaha sayniska iyo injineernimada of logarithms waxaa loo isticmaalaa wakiilnimo a more dabiiciga ah ee ifafaale jirka. Tusaale ahaan, si weyn loo yaqaan in ay isticmaalaan qiimaha qaraabo - desibelo markii qiyaasay xoogga sanqadha iyo iftiinka ee physics, baaxadda buuxda ee xiddigaha in pH ah ee kiimikada iyo kuwa kale.

xisaabinta logardam oggolyahay si fudud u hubin haddii ay qaataan, tusaale ahaan, iyo in lagu dhufto tiro shan lambar 3 "gacanta" (khaanadda a), iyadoo la isticmaalayo loox oo logarithms on xaashi of warqad iyo qaanuunka slide ah. Waxaa ugu Filan in aan idhaahdo in Xaalada danbe, xisaabinta doona xoogga 10 ilbiriqsi waa kan ugu yaab Waa maxay xaqiiqada ah in calculator casriga ah xisaabaha, kuwaas oo ay qaataan waqti, aan ka yarayn.