Uyini logarithm?

Ephakathi eyaziwa ngokuthi isikhathi travel futhi ezindawo okutholakele. Okuwukuphela kwendlela ukugcwaliseka elide travel ayewugibele ukuthi njalo elihlobene ne ukuqaliswa lemiqulu emikhulu navigation izibalo. Kunzima ukucabanga inqubo kokuzama izibalo ukubuyabuyelela, ukwahlukana senhlavu ezinhlanu-izinombolo "ngesandla". Dzhon Neper, isazi semfundiso yenkolo ngo ubunjalo ibhizinisi enkabeni yalo, wahlanganyela ezokungcebeleka izibalo Trigonometric ukuyichaza esikhundleni inqubo kukhathaza zokuphindaphinda ngo kwalokho elula. Yena ngokwakhe wathi umgomo wakhe wawuwukuba "balahle nobunzima futhi tedium izibalo, okuyinto sivimbele eziningi kusukela cwaningo wezibalo." Imizamo aphumelele - ithuluzi zezibalo ngokuthi logarithms uhlelo yadalwa.

Ngakho-ke yini i-logarithm? Ngesisekelo kathisha logarithmic kungenye ukumelwa: esikhundleni ezivamile Positioning System, njengoba sasivamise, inani A umelwe amandla yokukhuluma, lapho abanye nenombolo engafanele N, esibizwa ngokuthi i-base phuzu ephakanyiswe n degree, ukuthi umphumela A. inombolo Ngakho , n - iyona logarithm base N. Inketho isisekelo sesistimu yezinombolo icacisa igama uhlelo. Ukuze vichisleny elula esetshenziswa ohlelweni idesimali ka logarithms, futhi kwezesayensi nobuchwepheshe kabanzi simiso logarithms zemvelo, lapho base kuyinto engenangqondo inombolo e = 2,718. Inkulumo belinganisa logarithm inani A, e ilimi le-IiMbalo kulotshiwe kanje:

n = log (N) A, lapho N - base degree.

logarithms wezinombolo kanye zemvelo babe emibhalweni yabo ethize esifushanisiwe - lgA futhi lnA, ngokulandelana.

Izibalo uhlelo usebenzisa logarithms sibalo, element eyinhloko ukuguqulwa inamba ifomu amandla logarithms kwethebula abanye base, isibonelo 10. Lokhu zokukhwabanisa kuqondile. Okulandelayo, sebenzisa amandla nempahla izinombolo, owakhiwa yokuthi lapho siphindwe degree of isibaya sazo. In practice, lokhu kusho ukuthi ukuphindaphinda izinombolo nge ukumelwa logarithmic esikhundleni ngokungeza amandla abo. Ngakho-ke, umbuzo othi "yini-logarithm we" uma kuwukuthi bayaqhubeka "futhi kungani kudingeka ke," kuyinto impendulo elula - ukwenza lula inqubo ukubuyabuyelela-division of zamadijithi amaningi - I-kwalokho "ngo ikholomu" kuba lula kakhulu ukuba azale ande "ngo ikholomu". Ubani akakholelwa - mnike zama walala futhi anandise ezimbili izinombolo eziyisishiyagalombili-bit.

Ithebula lokuqala logarithms (base nge inombolo zemvelo), eyanyatheliswa ngo-1614 Dzhon Neper, futhi ngokuphelele mahhala amaphutha kukho futhi kuhlanganise ithebula logarithms ezivamile, wabonakala ngo-1857 futhi njengoba Bremikera ithebula ezaziwayo. Ukusebenzisa logarithms base ifomu inombolo engenangqondo ngoba inombolo, impela nje etholakale Taylor uchungechunge kokuba isicelo ebanzi e ebalulekile futhi umehluko calculus.

Ingqikithi zalesi simiso computer inikeza impendulo yombuzo othi, "Yini i-logarithm" futhi kusobala kusukela ubunikazi logarithmic eziyisisekelo: N (isizinda logarithm) ophakanyiswe emandleni n, ilingana logarithm inombolo A (logA), kule nombolo ilingana A. Kulokhu, A> 0, okusho logarithm kunqunywa kuphela izinombolo omuhle, futhi base lwamakholi uhlale engaphezu kuka-0 no-akulingani 1. Esekelwe osekushiwo, property logarithm engokwemvelo ingakleliswa kanje:

1. Inkambu logarithm engokwemvelo - konke-eksisi zezinombolo kusuka 0 infinity.
2. ln x = 0 - kuwumphumela ubuhlobo eyaziwa - iyiphi inombolo ka-zero degree 1.
3. ln (X * Y) = ln X + lnY - ebaluleke kakhulu yezamakhompyutha zokukhwabanisa impahla - logarithm komkhiqizo wezinombolo ezimbili Ramen isamba logarithms ngayinye.
4. ln (X / Y) = ln X - lnY - logarithm le quotient wezinombolo ezimbili kulingana umehluko we logarithms yezinombolo.
5. ln (X) n = n * ln X.
6. I-logarithm engokwemvelo kuyinto differentiable ayizindunduma umsebenzi phezulu, lapho ln 'X = 1 / X
7. log (N) A = K * ln A - logarithm ngokuvumelana iyiphi omuhle futhi ngaphandle isisekelo esingu-e emvelo kuyahluka kuphela kusukela isilinganiso.

Manje zonke wesikole uyazi okungukuthi logarithm, kodwa sibonga kwentuthuko emkhakheni izinkinga osetshenziswayo computer ubunjiniyela umsebenzi yezamakhompyutha sezedlule. Nokho, logarithms, kakade njengoba ithuluzi zezibalo esetshenziswa ukuxazulula zibalo nge angaziwa ku exponent ethi lokuthola isikhathi ukubola enemisebe izakhi nakwezinye izindawo wezibalo, i-physics kanye nezibalo.