Logarithm: ukubala njani?

Ubungakanani yamanani ngamnye siphelise zezibalo yavela kwiinkulungwane ezadlulayo. Wew kunye algebra idibana ezimbini iinketho - lesishumi kwaye see logarithm zendalo. Abalwa ifomula ezahlukeneyo, inxaki ngaphandle ngokubhala, usoloko ulingana omnye komnye. Le ungubani ichaza iimpawu ezinokuba luncedo ukuba amandla umsebenzi.

Iimpawu kunye iinkalo ezibalulekileyo

Kweli nqanaba ukwahlula iimpawu ezilishumi eyaziwa zemathematika. Eqhelekileyo kakhulu kwaye ethandwa kuzo zezi:

• Radicand yelog, lahlulwe ngenani nengcambu usoloko umnye njengoko logarithm eqhelekileyo √.
• imveliso yelog usoloko lilingane sum of yomvelisi.
• LG = enkulu elithile, phinda inani eyakhiwe kuwo.
• Ukuba uthe wakususa log tivi nomabi uya LG zabucala.

Ukongeza, kukho inxaki ngokusekelwe yesazisi engundoqo (ingqalelo iqhosha), kwinguqu esa kwisiseko ezihlaziyiweyo kunye neefomula eziliqela ezingephi.

Ukubalwa ilogarithm - yenjongo kunokuba ethile, ke ngoko, ukuba ukuhlanganiswa iimpawu kwi isisombululo kufuneka wasondela ngononophelo kwaye khangela qho izenzo zabo guquki. Asimele silibale ngayo iitafile, ekufuneka ukukhangela rhoqo wafumana khona ukuba bakhokelwe data kuphela.

Imihlobo term lwezibalo

Umahluko omkhulu nezibalo "ezifihliweyo" kwi isiseko (a). Ukuba ine isafobe ka-10, oko kukuthi i-log wokugqibela. Kwimeko esahlukileyo «kukho» uguqulwe "y" kwaye ngokudlul kunye neempawu ezingenangqondo. Kananjalo kubalulekile ukuba siqaphele ukuba ixabiso elililo ibalwa yi quadratic ezizodwa, apho ubungqina uba ithiyori bafunda ngaphaya kwikharityhulam yesikolo esiphakamileyo.

logarithm iidecimal uhlobo esisetyenziswa ngokubanzi kwi ekubaleni iifomyula ezintsonkothileyo. Yenziwe yonke itheyibhile lula izibalo baze kubonisa ngokucacileyo inkqubo yokusombulula le ngxaki. Ngelo xesha phambi inguqu eyiyo ukuya ishishini kufuneka ukwakha log ngendlela eqhelekileyo. Ukongeza, ngasinye senza ivenkile isikolo uyakwazi ukufumana umgca ekhethekileyo kunye abasakhasayo, ukunceda ukusombulula inxaki nayiphi xaka. Logarithm Briggovym ebizwa inombolo, okanye inombolo Euler, emva kokuba umphandi lowo kuqala yafunyanwa kwaye yapapashwa ixabiso yokubeka ecaleni ngemimmiselo ezimbini.

iintlobo ezimbini olungumgubo

Zonke iintlobo-ntlobo becomputing imisebenzi impendulo ukuba imeko log elide, abe kwigama elisecaleni ne isixhobo ngamandla zezibalo. equation kobudlelwano i ikopi phantse ngqo ubalo lwe logarithm olusezantsi, xa usibona izisombululo ezichanekileyo. Nje ngobuwena lokuqala kuquka inani ezizodwa, kuyanceda ukuqonda ngokukhawuleza lo mbandela, kwaye eyesibini ithatha indawo log kwi degree zesiqhelo. Le ubalo usebenzisa ifomula wokugqibela kufuneka ziquka ixabiso elitshintshayo.

Umahluko aqinile

Bobabini banendlela eziphambili iimpawu zazo index lwahlule phakathi omnye komnye:

• Logarithm. Inxalenye ebalulekileyo - ubukho imbopheleleko yenu kwisiseko. Standard Ixabiso version ilingana 10 ulandelelwano Iphawulelwe - x okanye lg x log.
• Natural. Ukuba nomzantsi walo ukungena «e», nto leyo rhoqo ubalwe efana ngqo equation apho n lujika ngokukhawuleza ngayo Infinity, ubukhulu elithelekelelwayo elingana yedijithali ka-2,72. Amanqaku ezisemthethweni, yamkelwa kokubini esikolweni kunye neefomula yobungcali entsonkothileyo kakhulu, - ln x.
• Ezahlukeneyo. Ngaphandle logarithm esisiseko kwenzeka hexadecimal kunye neentlobo lokubini (isiseko-16 no-2, ngokulandelelanayo). Kukho uguqulelo ezintsonkothileyo index isiseko 64, eziphantsi kolawulo eyondeleleneyo uhlobo olwenziwayo, ngobuciko zejometri uvelisa ukubalwa eziphumo zokuphela konyaka.

Isigama ibandakanya izixa zilandelayo ingxaki aljibra:

• ixabiso;
• ingxabano;
• base.

Ukubalwa log

Kukho iindlela ezintathu ngokukhawuleza ngomlomo ukwenza yonke ubalo eziyimfuneko ukufumana isiphumo ngomdla sisiphumo isigqibo mandatory tye. Ekuqaleni, lo logarithm omalunga oda yakho (irekhodi inani isidanga lwenzululwazi). ixabiso ngasinye HIV inokunikwa yi lenxaki, apho elingana mantissa (inani-1 ukuya ku-9) kwaye phinda ngo ezilishumi ukuya n-th isidanga. Le yokubala lobeko isekelwe kwizibakala ezimbini izibalo:

• imveliso kunye sum log nisoloko ngezinga elifanayo;
• logarithm athathwa amanani ukuya ezilishumi, ayikwazi igqithe ixabiso ku1.

1. Ukuba ngaba kwenzeke impazamo ekubaleni, ekubeni ungaze ube ngaphantsi kwesinye bejonge nokuthabatha.
2. Ukuchaneka lula xa umntu ecinga into yokuba LG isisekelo japan ezintathu zokugqibela - i-ube zizahlulo ezintlanu iyunithi. Ngoko ke, naliphi na ixabiso zezibalo mkhulu kuno-3 wongeza ngokuzenzekela impendulo enye into.
3. Phantse ukuchana okuzalisekileyo kufikelelwa ukuba ngesandla kwitafile ekhethekileyo ukuze kube lula ezisetyenziswa kwimisebenzi yabo novavanyo. Ingasetyenziswa ukufumanisa ukuba yintoni na logarithm wokugqibela kwi pesenti ezilishumi yenani lokuqala.

Imbali ye log yokwenene

ngenkulungwane yeshumi wakuva imfuneko ngaphezu ezimbaxa kunokuba iye yaziwa kwinzululwazi ngelo xesha. Oku kwakunjalo ngokukodwa kwicandelo multi-zixabisekile kwaye uphinda-phindo lwamanani kunye guquki enkulu, kuquka amaqhezu. Ekupheleni kwesiqingatha sesibini sale ixesha iingqondo ezininzi baye kwisigqibo sokuba Ukongeza kwamanani kwetafile, nto leyo uthelekisa ezimbini progressions: izibalo kunye nejiyometri. Kulo mzekelo, zonke izibalo ezisisiseko baba abut xabiso. Ngokufanayo, izazinzulu ziye zidityaniswe kunye nokuthabatha.

Sisihlandlo sokuqala lg yaqhutywa 1614. Kwenza andilociko yezibalo Napier ifani. Kubalulekile ukuqaphela ukuba, nangona popularization enkulu yeziphumo, ngempazamo ifomula ngenxa intswela ezinye iinkcazelo esele yenziwe ebonakala kamva. Baqalisa uphawu onamanani ezintandathu. Kufutshane ingqondo i logarithm ye abazalwana Bernoulli, yaye legitimizing bt kwenzeka kwinkulungwane elinesibhozo Euler. Kwakhona wakhupha osemqoka kwinkalo yemfundo.

Imbali ye log ezimbaxa

LG bt lizama nokuzibuyisela kwinginginya ezibanzi wenza ekuqaleni kwenkulungwane ye-18, Bernoulli kunye Leibniz. Kodwa ukuthembeka izibalo yeengcingane, akaba nako ukwenza. Ngesi sihlandlo, yonke le ngxoxo kwaqhutywa, kodwa inkcazelo ngqo inani kungabikho. Incoko liqale kamva, kodwa phakathi Euler kunye d'Alembert. Wesibili, kuloo mgaqo, bayavumelana ezininzi izibakala ezinikezelwa yi ngunozala ixabiso, kodwa ndicinga ukuba izalathi ezintle nezimbi linokulingana. Phakathi kwale formula ngenkulungwane bekubonakalisiwe njengoko ukhetho lokugqibela. Ngaphezu koko, Euler ithe yapapashwa logarithm kwaye azotywe yemizobo kuqala.

iitafile

Iimpawu ze inani ibonisa ukuba amanani multi-ixabiso alikwazi ukuzandisa, neloge ukufumana kwabo waza wabeka ngokusebenzisa amacwecwe zizodwa.

Gqitha eli nani yayikukuba ngeenkwenkwezi abasoloko benyanzeleka ukuba basebenze kunye iintlobo ngeentlobo ukulandelana. Kumaxesha Soviet logarithm wafuna ezikuqokelelo Bradis, yakhululwa ngowe-1921. Kamva, ngowe-1971, kwakukho kokupapashwa Vega.