Logarithm: mmene kuwerengera?

Mlingo wa manambala munthuyo ndi masamu akuti anayamba zaka zapitazo. Masamu ndi ajebura akukumana yachiwiriyo - decimal ndi logarithms achilengedwe. Iwo mopitirira mwa mitunduyi osiyana, anthu aone kuti pali ena kuposa kulemba, nthawi zonse ofanana ndi mnzake. amadziwikira umu ndi katundu amene ali othandiza kuti ntchito kuthekera.

Features ndi zinthu zofunika kwambiri

Pa nthawi imeneyi kusiyanitsa khumi kudziwika makhalidwe masamu. Ambiri ndi anthu ambiri awa:

• Radicand chipika, anagawa ndi mtengo wa muzu yofanana monga logarithm wamba √.
• chipika mankhwala nthawi zonse wofanana Uwerenge Mlengi.
• LG = waukulu pati, ndi kuchulukitsa chiwerengero cha chamangidwa mu izo.
• Ngati kuchotsapo chipika lopeza wogawira adzakhala LG payekha.

Komanso, pali aone kuti pali zochokera chizindikiro chachikulu (ankaona kiyi), kusintha kwa m'munsi kusinthidwa ndi kachitidwe angapo ang'onoang'ono.

Mawerengedwe a logarithm - cholinga m'malo yeniyeni Motero, kuphatikiza ya katundu mu njira ayenera kulankhula mosamala ndi kumaona zochita zawo ndi kugwirizana. Tisaiwale za matebulo, amene ayenera nthawi zonse onani napeza pali kutsogoleredwa deta chabe.

Zosiyanasiyana masamu akuti

Kusiyana waukulu wa masamu "zobisika" mu m'munsi pa (a). Ngati chithunzi cha 10, kuti ndi chipika decimal. Pankhani zosiyana «ndi» adziwonetsa "Y" ndipo ali transcendental ndi makhalidwe zopanda nzeru. Komanso Dziwani kuti phindu lenileni ndi kuchita masamu ndi aone kuti pali wapadera, pamene umboni amakhala chiphunzitso anaphunzira kupitirira maphunziro sekondale.

logarithms Decimal a mtundu chimagwiritsidwa ntchito mu mawerengedwe a mitunduyi zovuta. Anapanga tebulo lonse kuti magawowa anapezazo ndi amasonyeza ndondomeko zothetsera vutoli. Pa nthawi yomweyo pamaso kusintha enieni malonda ayenera kumanga chipika mu mawonekedwe muyezo. Komanso, aliyense amapereka sitolo sukulu mungapeze mzere wapadera ndi lonse, kuthandiza kuthetsa anthu aone kuti pali Kuvuta iliyonse. Logarithm Briggovym wotchedwa nambala, kapena Euler chiwerengero, pambuyo kafukufuku amene woyamba anatulukira ndi lofalitsidwa mtengo Kutchulira wa determinations awiri.

mitundu iwiri ya chilinganizo

Mitundu yonse ndi mitundu ya kompyuta ntchito ayankhe ndi chikhalidwe chipika akuti, ndi dzina osiyana ndi okhwima chipangizo masamu. Kwakukulu kwambiri aone kuti pali ndi buku pafupifupi yeniyeni ya mawerengedwe logarithmic, pamene kuonera njira yolondola. Monga chimake choyamba zikuphatikizapo angapo apadera, amathandiza mwamsanga kumvetsetsa nkhaniyo, ndipo chachiwiri m'malo chipika pa digiri wamba. kuwerengetsera ntchito chilinganizo yamasika pazikhalanso mtengo variable.

Kusiyana ndi terminology

Onse ndi waukulu awo index mbali kusiyanitsa pakati pa wina ndi mnzake:

• Logarithm. Mbali yofunika kwambiri - ndi lamulo pamaso pa maziko a. Wosasintha mtengo ndi wofanana 10. zaikidwa ndondomeko - fufuzani × kapena LG x.
• Natural. Ngati maziko ake ndi lowani «mauthenga», amene nthawi zonse masamu mosamalitsa zofanana kuti anthu aone kuti pali komwe N mofulumira kulingalira osawerengeka, pafupifupi kukula kwa lofanana digito wa 2,72. zizindikiro Official anavomera kusukulu ndi mu mitunduyi zovuta zambiri akatswiri - Ln x.
• Osiyana. Kuwonjezera logarithms zofunika zimachitika hexadecimal ndi mitundu bayinare (m'munsi 16 ndi 2, motero). Pali zovuta Baibulo ndi index m'munsi 64, kugwa pansi pa ulamuliro mwadongosolo mtundu dziphunzitsiranso, ndi zojambula mwatsatanetsatane ambabala mawerengedwe a zotsatira komaliza.

The terminology zikuphatikizapo zedi izi mu vuto algebraic:

• mtengo;
• mtsutso;
• m'munsi.

Mawerengedwe a chipika

Pali njira zitatu mwamsanga ndipo pakamwa kuchita kuwerengetsera zonse zofunikira kupeza chifukwa ndi chidwi zotsatira za chisankho kuvomerezedwa bwino. Poyamba, pafupifupi logarithm anu (mbiri sayansi chiwerengero cha digiri). Aliyense mtengo zabwino angaperekedwe ndi aone kuti pali kumene ndi wofanana ndi mantissa (nambala ya 1 mpaka 9) ndi kuchulukitsa ndi digiri khumi N-TH. mawerengedwe Izi zosinthika zachokera mfundo ziwiri masamu:

• mankhwala ndalama chipika nthawi zonse mlingo yemweyo;
• logarithm anatengedwa kuchokera manambala imodzi khumi, sangathe kupitiliza kufunika 1 Mfundo.

1. Ngati vuto mu mawerengedwe a zikuchitikadi, si zosakwana imodzi mu njira wochotsera.
2. Zowona kumatheka ngati momwe munthu alingaliririra LG m'munsi atatu chifukwa komaliza - zisanu magawo a amodzi. Choncho, phindu masamu ndi wamkulu kuposa 3 basi zimawonjezera yankho item wina.
3. Pafupifupi molondola wangwiro zimatheka ngati dzanja ndi tebulo apadera kuti mosavuta ntchito mu ntchito zawo kuwunika. Thiabendazole angagwiritsidwe ntchito kupeza zimene ndi logarithm decimal peresenti khumi la nambala pachiyambi.

Mbiri ya chipika weniweni

m'ma chakhumi ndi chisanu ndi chimodzi anali ndi mtima wofuna mawu zambiri zovuta kuposa wakhala kudziwika kwa sayansi pa nthawi imeneyo. Zimenezi zinali zoona makamaka Mipikisano ofunika magawano ndi chulutsa manambala ndi kugwirizana kwambiri, kuphatikizapo ting'onoting'ono. Kumapeto kwa theka lachiwiri la nyengo ya malingaliro angapo kuti afike pomvetsetsa kuti Kuwonjezera wa manambala mu gome, lomwe limanena awiri progressions: masamu ndi zojambula. Pankhaniyi anapezazo zonse zofunika anali abut phindu atsopano. Mofananamo, asayansi Integrated ndi wochotsera.

Kutchula koyamba za LG unachitikira mu 1614. Iwo anapanga zofufuzafufuza masamu Napier labambo. Dziwani kuti ngakhale popularization lalikulu la zotsatira, m'kusokera chilinganizo chifukwa cha umbuli wa ena a matanthauzo chaonekera kuti inatulutsidwa mochedwa. Iwo anayamba ndi chizindikiro zisanu ndi chithunzi. Pafupi ndi luntha la logarithm wa abale Bernoulli anali ndi legitimizing kuwonekera koyamba kugulu zinachitika m'zaka za m'ma chakhumi ndi chisanu ndi chitatu Euler. Iye chikalata mbali mu maphunziro.

Mbiri ya chipika zovuta

LG kuwonekera koyamba kugulu akufuna cigawo ku misa yotakata anachitira pa chiyambi cha m'ma 18, Bernoulli ndi Leibniz. Koma kukhulupirika kwa kuwerengetsera ongolankhula, iwo sangakhoze kupanga. Pa nthawiyi, kutsutsana lonse kunachitidwa, koma tanthauzo lenileni la chiwerengero cha osati kutenga n'kukagwiritsa. Kucheza adapitiriza ina, koma pakati Euler ndi d'Alembert. Yotsirizira anali, mfundo, amagwirizana ndi ambiri mfundo zoperekedwa ndi woyambitsa wa kufunika, koma ine ndikuganiza kuti zizindikiro zabwino ndi zoipa ayenera kukhala ofanana. Pakati pa chilinganizo izi m'ma izo akuonetsedwa ngati njira komaliza. Komanso, Euler otumphukira linasindikizidwa logarithm ndi zithunzi choyamba amakopeka.

matebulo

Katundu wa nambala amasonyeza kuti manambala Mipikisano mtengo sangathe muchuluke, chipika kuwapeza ndipo ndaika matebulo apadera.

Wofunika kwambiri chithunzi ichi chinali chifukwa zakuthambo amene akukakamizidwa ntchito ndi zosiyanasiyana mindandanda. Mu Soviet Union logarithm anafuna mu Bradis deta, linatuluka mu 1921. Kenako mu 1971, panali mabuku Vega.