I izakhiwo logarithms, noma emangalisayo - eduze ...

Isidingo Computing uvele umuntu ngokushesha, njengoba nje wakwazi ukubeka inani lezinto emzungezile. It kungenziwa bazitshela ukuthi ambalwa kokuhlaziywa logic zenza ukuba kancane kancane "add-ukhupha" isidingo uhlobo ukubala. Lezi izinyathelo ezimbili ezilula osemqoka ekuqaleni - zonke ezinye manipulations ngezinombolo eyaziwa ngokuthi ukubuyabuyelela, ukwahlukana, Exponentiation , njll - a "imishini" okulula ezinye algorithm yezamakhompyutha, okuncike izibalo ezilula - "phinda-ukhupha". Kungakhathaliseki ukuthi laliyini, kodwa ukudalwa algorithm for Computing kuyimpumelelo enkulu ukucabanga, futhi abalobi zabo ngeke phakade ziyabuthonya kwimemori lesintu.

Eziyisithupha noma eziyisikhombisa emakhulwini eminyaka adlule emkhakheni navigation zasolwandle kanye astronomy iye yandisa isidingo esiningi izibalo, okuyinto akumangalisi, ngoba it is eNkathini Ephakathi yaziwa ukuthuthukiswa navigation nesayensi yokuhlolwa kwezinkanyezi. Ukuhlala kugcinwe lo ibinzana "funa izinhlobo ukunikezela" zezibalo eziningana kwadingeka umbono - ukufaka esikhundleni ukusebenza kakhulu okhandlayo wokuphindaphinda ezimbili izinombolo elula kwalokho (dually kubhekwe umqondo esikhundleni division by ukukhupha). Le nguqulo usebenza entsha uhlelo Computing ukuthi ebekwe 1614 emsebenzini Dzhona Nepera ngesihloko emangalisayo kakhulu "Incazelo etafuleni ngendlela emangalisayo logarithms." Yiqiniso, ngcono eminye kohlelo olusha undendende, kodwa izakhiwo eziyisisekelo logarithms eyayibekelwe ngaphezulu Napier. Umqondo kuhlaziywa uhlelo usebenzisa logarithms kwaba ukuthi uma uchungechunge lwezinombolo yakha inchubekelembili weJiyomethri, logarithms yabo futhi yakha inchubekelembili, kodwa izibalo. Ephambi kwezinduna amatafula pre-eklanyelwe indlela entsha zokuhlala lula izibalo, futhi owokuqala slide rule (1620 ngonyaka) mhlawumbe wokubala lokuqala lasendulo futhi esebenza kahle kakhulu - ithuluzi ubunjiniyela esisemqoka.

Ukuze ukuphayona endleleni ogcwele izikhisi njalo. Ekuqaleni, le logarithm base likhishiwe ngempumelelo futhi ukunemba ukubala kwaba ongaphakeme, kodwa kakade 1624 etafuleni elicwengiweyo nge isizinda idesimali yashicilelwa. I izakhiwo logarithms zihlobene ngokuyisisekelo ekutholeni: logarithm b - C iyinombolo okuyinto, lapho degree of logarithm isizinda (inombolo A), okuholela eziningi b. Classic ukuqoshwa inketho libukeka: logA (b) = C - ukuthi ufunde kanje: b logarithm, base A, inombolo C. Ukuze isenzo usebenzisa hhayi ejwayelekile, inombolo logarithmic, odinga ukukwazi iqoqo imithetho, eyaziwa ngokuthi "izindawo logarithms. " Ngomqondo onabile, yonke imithetho abe subtext ezivamile - indlela ungengeza, ususe futhi uguqule logarithms. Manje siyazi indlela yokukwenza.

zero Logarithmic nokukodwa

1. logA (1) = 0, logarithm isibalo u-1 ilingana 0 nganoma yisiphi isizathu - yalokho ngqo wenombolo ephakanyiswe zero degree.

2. logA (A) = 1, logarithm okufanayo inombolo base 1 - yaziwa kahle kweqiniso ngenxa yanoma yisiphi isibalo amandla kuqala.

Kuhlanganisa nekususa we logarithms

3. logA (m) + logA (n) = logA (m * n) - isamba logarithms iyona logarithm izinombolo eziningana umsebenzi.

4. logA (m) - logA (n) = logA (m / n) - umehluko we logarithms yezinombolo, elifana langaphambilini, ilingana logarithm isilinganiso lezi zinombolo.

5. logA (1 / n) = - logA (n), i-logarithm we ephambene logarithm lalenamba silingana "lokususa". Kulula ukubona ukuthi lokhu kuwumphumela okuvela kuyo le nkulumo odlule 4 ngoba m = 1.

Kulula ukuqaphela ukuthi imithetho idinga 3-5 nhlangothi zombili base efanayo log.

Exponents ngokuya logarithmic

6. logA (mn) = n * logA (m), i-logarithm inani degree n uyalingana logarithm le nombolo, siphindwe okungekho n.

7. log (IzE) (b) = (1 / c) * logA (b), ifundwa ngokuthi "logarithm b, uma base ine uhlobo Ac, ilingana umkhiqizo logarithm base b futhi Inani reverse c».

Formula eshintsha base logarithm

8. logA (b) = - logC (b) / logc (A), logarithm b base A ngesikhathi sithola ukuthi ukwedlulela kuleso base C esibaliwe quotient ka-logarithm base b C no C logarithm nenombolo base ilingane odlule base A, lapho uphawu "lokususa".

I logarithms ngenhla kanye nezici zabo ukuvumela isicelo efanelekayo ukuba lula ukubala we afanayo ezinkulu ezinombolo, ngaleyo ndlela sinciphise isikhathi izibalo zezinombolo futhi inikeza ukunemba eyamukelekayo.

Akumangazi ukuthi esayense nobunjiniyela izakhiwo logarithms zisetshenziselwa ngaphezulu ukumelwa yemvelo imihlola ngokomzimba. Ngokwesibonelo, eyaziwa emhlabeni wonke ukusebenzisa amanani isihlobo - decibel angu lapho kulinganiswa umfutho umsindo nokukhanya kuyi-physics, ubukhulu ngokuphelele ukufunda izinkanyezi e pH kwamakhemikhali kanye nabanye.

Kusebenta kathisha logarithmic kalula ukuhlola uma ukuthatha, isibonelo, futhi anandise inombolo idijithi emihlanu-3 "ngesandla" (e ikholomu), usebenzisa amathebula logarithms ku ephepheni kanye slide rule. Engingakusho nje ukuthi Kulo mBhalo, ukubala kuzothatha ekuqineni imizuzwana 10 Okumangazayo nakakhulu ukuthi wokubala yesimanje lezi izibalo kuthathe isikhathi, hhayi kancane.