Logarithm: sei kuverenga?

Mwero mumwe nhamba iri kwemasvomhu izwi sezvaari emakore akapfuura. The geometry uye nemasvomhu rinoungana maviri zvokusarudza - grade uye zviwanikwa logarithms. Vari akaverenga ne Masvomhu siyana, mukana wokuti vanhu vanga vamwe pane kunyora, anogara kuenzana mumwe. Kuzivikanwa uku rinorondedzera ehupfumi zvinobatsira dzingangoitika basa.

Features uye zvinokosha chaizvo

Panguva iyi kusiyanisa gumi anozivikanwa kwemasvomhu unhu. Vakawanda uye yakakurumbira pane aya:

• Radicand nerogi, yakakamurwa kukosha mudzi anogara kufanana vanhuwo logarithm √.
• danda chigadzirwa anogara akaenzana makuru anogadzira zvinhu.
• Lg = pakukura pamwero, kubudikidza vachiwedzera uwandu inovakwa mariri.
• Kana uchibvisa cherogi dividend mugoveri kuchaita LG voga.

Uyezve, pane mukana wokuti vanhu vanga inobva huru ani (vaiona kiyi), yezwi yoku- nechigadziko uye wandei Masvomhu zviduku.

Kukarukureta of logarithm - a nani chaizvo chinangwa, saka, kuti kudyidzana pakati zvivako zviri mhinduro inofanira kuswedera nokungwarira uye kugara zviito zvavo uye kusachinja-chinja. Hatifaniri kukanganwa pamusoro matafura, izvo vanofanira kuramba dzikawana imomo kuti vatungamirirwe chete mashoko.

Mhando kwemasvomhu izwi

The chikuru kusiyana kwemasvomhu "yakavanzwa" pangoro (a). Kana ane dimikira 10, kuti ndiye grade cherogi. In nevakomana nyaya «munhu» iri kuva "Y" uye ane transcendental uye musoro maitiro. Uyewo kucherechedza kuti chaiko ukoshi rinowanikwa nevanhu chinokosha mukana wokuti vanhu vanga, apo uchapupu anova dzidziso akadzidza kupfuura chesekondari hweutungamiri.

Grade logarithms ari mhando zvinowanzoshandiswa dzemaitirwe pakati Masvomhu dzakaoma. Vaiumba tafura yose aivabatsira Masvomhu uye kuratidza zvakajeka muitiro kugadzirisa dambudziko. Panguva iyoyo isati chaiko yezwi mabhizimisi anofanira kuvaka danda riri mureza chimiro. Uyezve, mumwe chitoro chikoro rinopiwa unogona kuwana chaiyo maererano scale, achibatsira kugadzirisa mukana wokuti vanhu vanga upi kunzwisisa. Logarithm Briggovym akadana nhamba, kana Euler nhamba, mushure muongorori uyo vokutanga yakawanikwa uye kubudiswa ukoshi juxtaposition kuti determinations maviri.

Two mhando fomura

mhando dzose uye akasiyana kadambari mabasa norudaviro kuva mamiriro rokuti danda, vane yoga zita uye zvakaoma kwemasvomhu mudziyo. Exponential mukana wokuti vanhu vanga chiri anenge chaiyo kopi theorem kukarukureta, kana ukatarira zvakarurama dambudziko. Just wokutanga musimboti rinosanganisira dzinoverengeka unyanzvi hwakasiyana, zvinobatsira nokukurumidza kunzwisisa nyaya, uye wechipiri unotsiva danda panguva zvavo dhigirii. Masvomhu kushandisa ekupedzisira payakavakirwa inofanira kusanganisira shanduka ukoshi.

Musiyano uye mazwi

Vose vane zvavo huru indekisi zvinhu kuzivisisa pakati imwe:

• Logarithm. Chinokosha - muite kuvapo nechimwe. Standard Version mutengo akaenzana 10. akanzi kutevedzana - X kana LG X danda.
• Natural. Kana chawo ari kusaina «E», inova dzose dzaona zvachose kufanana kuti mukana wokuti vanhu vanga apo N yava vaitovavarira kusaverengeka, iyo inofungidzirwa ukuru digitaalinen nerokuti 2,72. Official mavanga, vakagamuchirwa vaviri kuchikoro uye mune mamwe kunzwisisa nyanzvi Masvomhu, - Dr x.
• Siyana. Kunze dzinokosha logarithms kuchiitika hexadecimal uye binary mhando (chawo 16 uye 2, ukuwo). Pane kunzwisisa shanduro imwe chawo Indekisi 64, akawira pasi hurongwa kudzora adaptive mhando, pamwe geometric nemazvo unobereka dzemaitirwe yokupedzisira mugumisiro.

The mazwi zvinosanganisira zvinotevera kwazvo muna algebraic dambudziko:

• ukoshi;
• nharo;
• hwaro.

Kukarukureta kuti danda

Pane nzira nhatu kuti nokukurumidza uye nomuromo kuita zvakafanira zvose Masvomhu ari kuwana mugumisiro kufarira mugumisiro chisarudzo fanira zvakanaka. Pakutanga, fungidzira logarithm murayiro wenyu (chinyorwa esayenzi nokuwanda dhigirii). Mumwe zvakanaka ukoshi inogona inopiwa mukana wokuti vanhu vanga, apo akaenzana mantissa (nhamba 1 kusvika 9) uye kuwedzera gumi kusvika N-fung dhigirii. Izvi musiyano wezvinyorwa kukarukureta kunobva maviri kwemasvomhu chokwadi:

• chigadzirwa uye makuru nerogi nguva dzose kuva mwero chete;
• logarithm akatorwa kubva nhamba imwe gumi, unogona haapfuuri kukosha 1 pfungwa.

1. Kana chikanganiso dzemaitirwe zvinoitika, hachisi asingasviki mumwe nenzira kubvisa.
2. Kururama kunowedzerwa kana anofunga kuti LG chawo ane nhatu chokupedzisira mugumisiro - a-zvegumi mashanu ane chimwe. Saka, chero kwemasvomhu ukoshi mukuru 3 rwoga kunowedzera mhinduro imwe chinhu.
3. Anenge akakwana zvakarurama kunokwanisika kana ruoko ari kushandiswa tafura inogona nyore kushandiswa kuongorora mabasa avo. Inogona kushandiswa kuwana chii grade logarithm kusvika gumi muzana pakutanga nhamba.

Nhoroondo danda chairo

Nemitanhatu remakore ainzwa kudiwa dzakaoma mashoko pane yave nesayenzi panguva iyoyo. Izvi zvakanga kunyanya ichokwadi multi-vanokosheswa weboka uye chokuwanziridza nhamba pamwe kusachinja-chinja zvikuru, kusanganisira zvikamu zviduku. Panoperera yechipiri yezana nguva vakawanda pfungwa vakasvika pakugumisa kuti kuwedzera nhamba iri tafura, iyo rinofananidza maviri progressions: svomhu uye geometric. Panyaya iyi, zvose dzinokosha Masvomhu vaiva abut azvino ukoshi. Saizvozvowo, masayendisiti revatema uye kubvisa.

The kutaurwa LG yokutanga yakaitwa 1614. It akaita mudzidzi yemasvomhu Napier unonzi. Zvinokosha kucherechedza kuti, pasinei popularization chikuru zvabuda, iri nzira kukanganisa nokuda kusaziva mamwe tsanangudzo raitwa kuti akazviratidza gare gare. Zvakatanga aine-nhamba nhanhatu chiratidzo. Pedyo kunzwisisa logarithm of Bernoulli hama dzakanga, uye legitimizing debut kwakaitika nemasere remakore Euler. Naiyewo atara zvakakurumbira mumunda dzidzo.

Nhoroondo zvakaoma cherogi

Lg debut kuedza nokusangana kupinda dzakafara makuru dzimwe kwezana remakore rechi18, Bernoulli uye Leibniz. Asi kuvimbika yokungotaura Masvomhu, havana kugona kuita. Pachiitiko ichi, wose gakava chaiitirwa, asi chaiyo tsanangudzo nokuwanda asina kutorwa. Kukurukurirana vakatangazve Papera asi pakati Euler uye d'Alembert. The yokupedzisira yakanga, pfungwa, vanobvuma vakawanda chokwadi zvaipiwa muvambi mutengo, asi ndinofunga kuti zvakanaka uye kunaka zviratidzo zvinofanira kuenzana. Pakati remakore rino nzira zvakanzi kuratidzwa sezvo yokupedzisira kuzvipedza. Uyezve, Euler rinobva yakabudiswa logarithm uye Graphics vokutanga yakavhomorwa.

matafura

Properties pamusoro nhamba kunoratidza kuti multi-ukoshi nhamba havagoni uwande, nerogi kudzitsvaka ndokuisa kuburikidza specialized pamatafura.

Kunyanya zvinokosha mufananidzo uyu chaiva vanodzidza nezvenyeredzi vari kumanikidzwa kushanda akasiyana siyana sequences. In Soviet nguva logarithm vakatsvaka muna Bradis muunganidzwa, rakabudiswa muna 1921. Gare gare, muna 1971, pakanga bhuku Vega.