Logarithm: kanjani ukubala?

I degree of izinombolo ngabanye yigama zezibalo waqamba emakhulwini eminyaka adlule. I-geometry ne-Aljibhra ihlangabezana ezimbili ongakhetha - idesimali futhi logarithms zemvelo. Basuke libalwe amafomula ezahlukene, ezothando ngaphandle lokubhala, njalo ulingana nomunye. Lokhu ungubani uchaza izakhiwo ukuthi ziwusizo umsebenzi ezingaba khona.

Izici kanye izici ezibalulekile

Kuleli qophelo ukuhlukanisa izimfanelo eziyishumi zezibalo ezaziwayo. Okuvame kakhulu kanti ethandwa zazo yilezi:

• Radicand lwamakholi, zihlukaniswe ukubaluleka impande njalo kuyafana logarithm ezivamile √.
• lwamakholi umkhiqizo uhlale ilingana nenani lezinombolo umenzi.
• Lg = ngokwezinga elikhulu, ngokuvele azalane inani elakhiwa kuwo.
• Uma uthatha kude lwamakholi idividendi ehlukanisayo ngeke LG yangasese.

Ngaphezu kwalokho, kukhona equation okusekelwe ungubani main (kubhekwe ukhiye), sithola ukuthi ukwedlulela kuleso base olusha kanye namafomula eziningana ezincane.

Ukubalwa logarithm - umgomo kunalokho othize, ngakho-ke, ukuhlanganiswa sezindawo ikhambi kumele wasondela ngokucophelela futhi ihlole izenzo zabo futhi ukungaguquguquki. Akufanele sibakhohlwe mayelana amatafula, okuyinto badinga hlola, zathola khona ukuqondiswa idatha kuphela.

Izinhlobonhlobo eside zezibalo

Umehluko oyinhloko zezibalo "ocashe" kuyi-isizinda (a). Uma it has a sibalo 10, okungukuthi log ledesimali. Endabeni okuphambene «a» uguqulwe "y" futhi has obabazekayo nezici engenangqondo. Kubalulekile ukuqaphela ukuthi ukubaluleka langempela ibalwa kwesibalo ekhethekile, lapho ubufakazi iba imfundiso yokuziphendukela wafunda ngale lwezifundo samabanga aphakeme.

logarithms Idesimali yohlobo kabanzi kulesi sibalo amafomula ayinkimbinkimbi. Made kuze lonke etafuleni lula izibalo bese ubonisa ngokucacile inqubo yokuxazulula le nkinga iyabheda. Ngesikhathi esifanayo ngaphambi ushintsho soqobo ibhizinisi idinga ukwakha log efomini ejwayelekile. Ngaphezu kwalokho, ngamunye izimpahla esitolo esikoleni ungathola umugqa obukhethekile esikalini, isize ekuxazululeni ezothando yanoma yimuphi yinkimbinkimbi. Logarithm Briggovym ngokuthi inombolo, noma inombolo ka-Euler, ngemva umcwaningi owasungula lokuqala watholwa futhi wanyatheliswa ukubaluleka juxtaposition determinations ezimbili.

Izinhlobo ezimbili zezintuthwane ifomula

Zonke izinhlobo nezinhlobonhlobo Computing imisebenzi impendulo kokuba lwamakholi isimo eside, abe negama ehlukile futhi azinabo kudivayisi zezibalo. equation Exponential ikhophi cishe esiqondile ukubala logarithmic, lapho libhekwa izixazululo ezifanele. Vele samuntu sokuqala sihlanganisa eziningana ezikhethekile, kuyasiza ukuqonda ngokushesha isihloko sokufundisa, kanye yesibili ubuyisela log ngesikhathi degree abavamile. Izibalo kusetshenziswa indlela yokugcina kuzomele sifake inani lefonti.

Umehluko futhi amagama

Bobabili babe siqu izici zabo Inkomba esemqoka evelela phakathi nomunye:

• Logarithm. Ingxenye ebalulekile yokuphikelela - khona oyisibopho isisekelo. Standard okufushane ukubaluleka ilingana 10. ukulandelana Kulebulwe - log x noma lg x.
• Yemvelo. Uma isizinda salo ngemvume «e», okuyinto njalo ibalwa ngokuqinile ezifanayo kuya equation lapho n is ngokushesha amabombo infinity, lemakethe yama okulingana digital 2,72. izimpawu Esemthethweni, bamukela kokubili esikoleni futhi amafomula professional ebudisi - ln x.
• Ezahlukene. Ngaphandle logarithms eziyisisekelo kwenzeke-hexadecimal nezinhlobo kanambambili (isizinda 16 no-2, ngokulandelana). Kukhona ukulandisa eziyinkimbinkimbi nge Inkomba kumila 64, ewela ngaphansi kolawulo esihleliwe uhlobo oluhambelana, ngobuciko weJiyomethri ukhiqiza ekubalweni umphumela wokugcina.

I amagama kuhlanganisa nenani elandelayo inkinga algebraic:

• Inani;
• agumenti;
• isizinda.

Ukubalwa lwamakholi

Kunezindlela ezintathu ngokushesha futhi ngomlomo ukwenza zonke izibalo ezidingekayo ukuthola yi ngesithakazelo umphumela isinqumo saziso kwesokudla. Ekuqaleni, logarithm eseduze oda lakho (irekhodi yesayensi inani degree). Inani ngalinye omuhle kungenziwa okunikezwa equation, lapho ilingane mantissa (inani 1 kuya 9) futhi yanda ngezinkulungwane eziyishumi kuya n-th degree. Lokhu kubalwa okufana kusekelwe amaqiniso amabili zezibalo:

• umkhiqizo kanye sum lwamakholi njalo elifanayo;
• logarithm othathwe omunye izinombolo eziyishumi, awukwazi ukudlula ukubaluleka 1 iphuzu.

1. Uma iphutha kulesi sibalo kwenzeka, alilokothi engaphansi bebheke nokukhipha.
2. Ukunemba luphakanyiswa uma ubheka ukuthi LG isizinda has yi ezintathu zokugcina - a-eshumini ezinhlanu iyunithi. Ngakho-ke, noma iliphi inani zezibalo mkhulu kunezinhliziyo 3 ngokuzenzakalela kunezela impendulo into eyodwa.
3. Cishe ukunemba okuphelele abayifunayo uma isandla yitafula ezikhethekile ukuthi kungenziwa kalula ezisetshenziswa emisebenzini yabo kokuhlaziywa. Ingasetshenziselwa ukuthola ukuthi yini-logarithm ledesimali amaphesenti ayishumi of inombolo yokuqala.

Umlando ilogi yangempela

ngekhulu leshumi nesithupha wawuzwa ngokujulile isidingo ngaphezulu ngokuya eziyinkimbinkimbi kuka yaziwa isayensi ngaleso sikhathi. Lokhu kwenzeka ngokukhethekile division multi-ezaziswayo ukubuyabuyelela izinombolo nge ukungaguquguquki omkhulu, kuhlanganise izingxenyana zaso. Ekupheleni engxenyeni ngenkathi izingqondo amaningi yesibili sebefike esiphethweni sokuthi kwalokho izinombolo kuthebula, okuyinto eliqhathanisa ezimbili Progressions: izibalo kanye weJiyomethri. Kulokhu, zonke izibalo eziyisisekelo babe Abut ukubaluleka yakamuva. Ngokufanayo, ososayensi baye ihlanganiswe nokukhupha.

Lapho kukhulunywa ngaye okokuqala lg wawuba ngasekuqaleni 1614. Kungenze amateur sezibalo Napier nesibongo. Kuyaphawuleka ukuthi, naphezu popularization omkhulu ngemiphumela, ngesiphambeko ifomula ngenxa zokungazi ezinye izincazelo lwenziwe ukuthi uvele kamuva. Yaqala lapho uphawu eziyisithupha-sibalo. Esiseduzane ukuqonda logarithm abazalwane Bernoulli babengabakho, legitimizing DEBUT kwenzeka ekhulwini weshumi nesishiyagalombili Euler. Wabuye wakhipha sici emkhakheni wezemfundo.

Umlando lwamakholi eziyinkimbinkimbi

Lg aseqala ezama ukuhlanganisa uquqaba ezibanzi benza ekuqaleni kwekhulu le-18, Bernoulli futhi Leibniz. Kodwa ubuqotho izibalo ze-theory, abazange bakwazi ukwenza. Kulesi senzakalo, wonke mpikiswano lwenziwe, kodwa incazelo esiqondile inani hhayi ngokwesabelo esigunyaziwe. Ingxoxo uqalisiwe kamuva, kodwa phakathi Euler futhi d'Alembert. Lesi sakamuva kwaba isimiso esitholakala neziningi amaqiniso anikezwa umsunguli yenani, kodwa ngicabanga ukuthi izinkomba emihle nemibi zilingane. Phakathi kule formula ekhulwini ke saboniswa njengoba ukhetho sokugcina. Ngaphezu kwalokho, Euler esuselwe yanyatheliswa logarithm kanye ihluzo yokuqala edonswe edonswe kulezo.

amathebula

Properties of inombolo ubonisa ukuthi izinombolo multi-value abakwazi nande, log ngibafuna ngikhipha amathebula ayisipesheli.

ezibalulekile Ikakhulukazi lokhu babengamaphesenti ngoba izazi zezinkanyezi eziphoqelelwa ukusebenza ezihlukahlukene ukulandelana. Ezikhathini zaseSoviet logarithm ifuneka Bradis iqoqo, eyakhululwa ngo-1921. Kamuva, ngo-1971, kwaba khona ukushicilelwa Vega.