The katundu wa logarithms, kapena chodabwitsa - pafupi ...

Kufunika kompyuta anaonekera munthu pomwepo, mwamsanga pamene iye anatha kuchuluka kwa zinthu pa iye. Izo zikhoza kapadera kuti kachulukidwe kuwunika mfundo pang'onopang'ono zinachititsa kuti "kuwonjezera-kuchotsera" kufunika kwa mtundu wa mawerengedwe. Izi masitepe awiri osavuta ziri zofunikira poyamba - mwai ena onse ndi manambala kudziwika monga chulutsa, magawano, exponentiation , etc. - losavuta "mechanization" ena ma aligorivimu zowerengera, zomwe ndi zochokera odziwa - "pindani-kuchotsera". Chirichonse chimene icho chinali, koma chilengedwe cha ma aligorivimu kwa kompyuta ndiko Kupambana akuluakulu a ganizo, olemba awo nthawizonse kusiya chizindikiro awo kukumbukira anthu.

Isanu ndi umodzi kapena zaka zapitazo m'munda wa navigation apanyanja ndi zakuthambo chawonjezeka kufunika yambiri anapezazo, zomwe sizodabwitsa chifukwa amadziwika kuti Zapakati chitukuko cha navigation ndi zakuthambo. Pogwirizana ndi "kotunga kufunika Mitundu" Mawu masamu angapo anali lingaliro - m'malo ntchito kwambiri ntchito-tima Yochulutsa awiri manambala losavuta Kuwonjezera (dually ankaona lingaliro m'malo magawano ndi wochotsera). Baibulo ntchito za dongosolo latsopano kompyuta chinakhazikitsidwa mu 1614 mu ntchito ya Dzhona Nepera ndi mutu wochititsa chidwi kwambiri "Kufotokozera za tebulo chodabwitsa logarithms." Kumene, kusintha zina za dongosolo latsopano kunkangopitirira, koma katundu yaikulu ya logarithms anaperekedwa zambiri Napier. Ganizo kuwerengetsa dongosolo ntchito logarithms chinali ngati mndandanda wa manambala ndipamene kupitilira zojambula, logarithms awo komanso kupanga kupitilira, koma masamu. Pamaso pa matebulo chisanadze cholinga njira yatsopano ya kuthetsa wosalira anapezazo, ndipo woyamba Wopanda ulamuliro (1620 chaka) mwina woyamba wakale ndi kwambiri kothandiza Chiwerengero - kofunika kwambiri zomangamanga chida.

Pakuti upainiya msewu zonse ndi maenje. Poyamba, logarithm maziko a watengedwa bwinobwino ndi lolondola mawerengedwe anali otsika, koma kale mu 1624 tebulo woyengeka ndi maziko decimal anasindikizidwa. The katundu wa logarithms zichokera kwa kwenikweni kudziwa: logarithm wa B - C ndi nambala imene mlingo wa logarithm m'munsi (nambala A), chifukwa zingapo za b. Classic kujambula njira zikuwoneka ngati: logA (b) = C - kuti kuwerenga motere: b logarithm, m'munsi A, ndi chiwerengero cha C. Pofuna kuchita kanthu ndi ntchito bwinobwino ndithu, nambala logarithmic, muyenera kudziwa malamulo, lotchedwa "katundu logarithms. " Mfundo malamulo onse chimodzi subtext - mmene kuwonjezera, kuchotsera ndipo ambweza logarithms. Tsopano ife tikudziwa momwe angachitire izo.

Logarithmic ziro ndi chimodzi

1. logA (1) = 0, ndi logarithm chiwerengero cha 1 ndi wofanana 0 chifukwa chirichonse - Chifukwa cha nambala anamuukitsa kwa digiri ziro.

2. logA (A) = 1, logarithm chomwecho ndi chiwerengero m'munsi 1 - amadziwikanso odziwika woona kwa chiwerengero cha mphamvu choyamba.

Kuwonjezera ndi wochotsera wa logarithms

3. logA (m) + logA (n) = logA (m * n) - Uwerenge logarithms ndi logarithm a manambala angapo ntchito.

4. logA (m) - logA (n) = logA (m / n) - kusiyana kwa logarithms a manambala, wofanana ndi m'mbuyomu, ndi wofanana ndi logarithm wa chiŵerengero cha manambala awa.

5. logA (1 / n) = - logA (n), ndi logarithm wa osiyanitsidwa wa logarithm wa nambala iyi ndi wofanana ndi "opanda". N'zosavuta kuona kuti ndi chifukwa cha mawu akuti yapita 4 mamita = 1.

N'zosavuta kuona kuti malamulo amafuna 3-5 mbali zonse za yemweyo chipika m'munsi.

The exponents mawu logarithmic

6. logA (MN) = N * logA (m), ndi logarithm chiwerengero cha digiri N chofanana ndi logarithm wa nambala iyi, kuchulukitsa ndi yemwe amalimbikitsa N.

7. chipika (Mac) (b) = (1 / c) * logA (b), ndi kuwerenga kuti "logarithm wa b, ngati m'munsi ali mawonekedwe Mac, wofanana ndi mankhwala a logarithm ndi patsinde pa B ndi chiwerengero cha n'zosiyana m'ma».

Chilinganizo amasintha logarithm m'munsi

8. logA (b) = - logC (b) / logc (A), logarithm wa b m'munsi pa kusintha kwa m'munsi C kuchita masamu ngati quotient wa logarithm ndi m'munsi b C ndi C ndi logarithm ndi m'munsi chiwerengero wofanana ndi yapita m'munsi A m'mene ndi chizindikiro "opanda".

The logarithms pamwamba ndi katundu wawo mpata ntchito yabwino wosalira ndi mawerengedwe a lalikulu magulu M'ndandanda, potero kuchepetsa nthawi ya anapezazo ndi n'zosangalatsa kumva ndiponso limapereka zovomerezeka molondola.

N'zosadabwitsa kuti sayansi ndi zomangamanga katundu wa logarithms ntchito kwambiri chifaniziro zachilengedwe zodabwitsa thupi. Mwachitsanzo, wotchuka kugwiritsa ntchito mfundo wachibale - decibels pamene anayeza mwamphamvu phokoso ndi kuwala sayansi, ukulu mtheradi mu zakuthambo mu pH mu umagwirira ndi ena.

Efficacy logarithmic masovedwe mosavuta fufuzani ngati kutenga Mwachitsanzo, ndi kuchulukitsa zisanu manambala nambala 3 "pamanja" (mu mzati), ntchito matebulo a logarithms pa pepala ndi Wopanda ulamuliro. Wokwanira kuti mu Zikatero, mawerengedwe adzatenga pa mphamvu ya masekondi 10 Kodi Chodabwitsa kwambiri n'chakuti mu Chiwerengero ano kuwerengetsera izi nthawi, osati zochepa.