{"id":3287,"date":"2012-02-21T00:26:35","date_gmt":"2012-02-20T22:26:35","guid":{"rendered":"http:\/\/www.ilkkimbuldu.com\/?p=3287"},"modified":"2018-09-27T22:15:59","modified_gmt":"2018-09-27T20:15:59","slug":"logaritmayi-kim-buldu","status":"publish","type":"post","link":"https:\/\/www.ilkkimbuldu.com\/?p=3287","title":{"rendered":"Logaritmay\u0131 kim buldu"},"content":{"rendered":"

Logaritma on yedinci y\u00fczy\u0131l\u0131n ba\u015f\u0131nda hesaplar\u0131 h\u0131zland\u0131rmak i\u00e7in ke\u015ffedilen bir matematik y\u00f6ntemidir. Logaritma 300 y\u0131ldan daha uzun bir zaman boyunca temel bir hesap metodu olmu\u015ftur. On dokuzuncu y\u00fczy\u0131lda masa hesap makinalar\u0131n\u0131n do\u011fu\u015fu ve yirminci y\u00fczy\u0131lda elektronik hesap makinalar\u0131n\u0131n ortaya \u00e7\u0131k\u0131\u015f\u0131, logaritmaya olan ihtiyac\u0131 azaltm\u0131\u015ft\u0131r. Ancak logaritmik fonksiyonlar\u0131n teorik ve uygulamal\u0131 matematikte \u00f6zel bir yeri vard\u0131r.<\/p>\n

Logaritma, birbirinden habersiz \u00e7al\u0131\u015fan iki ki\u015fi taraf\u0131ndan ke\u015ffedilmi\u015ftir. Bunlar; 1614\u2019te \u0130sko\u00e7yal\u0131 John Napier<\/strong> ve 1620\u2019de \u0130svi\u00e7reli Joost B\u00fcrgi<\/strong>\u2019dir.<\/p>\n

John Napier<\/a><\/h3>\n

\"john-napier\"<\/p>\n

John Napier,\u00a0 isko\u00e7yal\u0131 matematik\u00e7i ve mucittir. 1550 – 1617 y\u0131llar\u0131 aras\u0131nda ya\u015fad\u0131. 1614\u2019te yazd\u0131\u011f\u0131 Mirifici Logarithmorum Canonis Descriptio (Logaritma Kurallar\u0131n\u0131n Tan\u0131m\u0131)<\/strong> adl\u0131 eserinde aritmetik ve geometrik dizinin kar\u015f\u0131la\u015ft\u0131r\u0131lmas\u0131yla, matemati\u011fe logaritma kavram\u0131n\u0131 getirdi. G\u00fcn\u00fcm\u00fczdekilerden farkl\u0131 olarak kurulan bu diziler, logaritmay\u0131, say\u0131n\u0131n azalan bir fonksiyonu olarak tan\u0131ml\u0131yordu.<\/p>\n

Oxford \u00fcniversitesi matematik profes\u00f6r\u00fc Briggs, Napier\u2019in Logaritma tablolar\u0131n\u0131 inceledi geli\u015ftirdi.\u00a0Basitle\u015ftirdi\u011fi logaritma cetvellerini Napier\u2019e\u00a0sunmak i\u00e7in Edinburgh\u2019a gitti. Napier 1618 ve Briggs 1624\u2019te kusursuz iki logaritma cetveli yay\u0131mlad\u0131.<\/p>\n

Joost B\u00fcrgi (1552 – 1632)<\/strong><\/h4>\n

\u00d6zellikle Kassel ve Prag’daki saraylarda faaliyet g\u00f6steren bir \u0130svi\u00e7reli saat \u00fcreticisi, astronomi \u00f6l\u00e7\u00fcm cihazlar\u0131 yapan bir matematik\u00e7idir. B\u00fcrgi, Napier’den farkl\u0131 bir y\u00f6ntemle, John Napier’den ba\u011f\u0131ms\u0131z olarak antilogaritma olarak bilinen bir ilerleme tablosu olu\u015fturdu. Napier, 1614’te ke\u015ffini yay\u0131nlad\u0131. B\u00fcrgi’nin Johannes Kepler’\u0131n emriyle kendi logaritma tablolar\u0131n\u0131 yay\u0131nlad\u0131\u011f\u0131 zaman\u00a0Napier’in Logaritmas\u0131 Avrupa’da yayg\u0131n bir \u015fekilde kullan\u0131lmaya ba\u015flanm\u0131\u015ft\u0131. B\u00fcrgi, 1600 civar\u0131nda kendi ilerleme tablosunu in\u015fa etmi\u015f olmas\u0131na ve B\u00fcrgi’nin \u00e7al\u0131\u015fmas\u0131 Napier’lerle ayn\u0131 amaca hizmet etmesine ra\u011fmen, logaritmalar\u0131n teorik bir temeli de\u011fildir. Bir \u00e7ok kaynak B\u00fcrgi’nin bir logaritmik fonksiyonun net bir kavram\u0131n\u0131 geli\u015ftirmedi\u011fini ve bu nedenle de logaritmalar\u0131n bir mucidi olarak g\u00f6r\u00fclemeyece\u011fi belirtilmektedir. Yine de \u00e7al\u0131\u015fmalar\u0131 nedeniyle Ay y\u00fczeyinde bir kratere Byrgius<\/strong> ad\u0131 verilerek ismi onurland\u0131r\u0131lm\u0131\u015ft\u0131r.<\/p>\n

Logaritma nedir?<\/h3>\n

Logaritmay\u0131 a\u00e7\u0131klamak i\u00e7in 2x2x2= 8 ifadesine bakal\u0131m. Bu 23= 8 olarak k\u0131saca yaz\u0131labilir. Bu \u00f6rnekte 3, 8\u2019in 2 taban\u0131na g\u00f6re logaritmas\u0131 denir. E\u011fer logaritma 10 taban\u0131na g\u00f6re olursa, bu logaritma basit logaritma veya ke\u015ffeden Henry Briggs<\/strong>\u2019e izafeten Briggs logaritma denir.\u00a0 Basit logaritma; 102= 100, 103= 1000, 104= 10000 e\u015fitliklerine dayan\u0131r.<\/p>\n

Logaritma kullan\u0131larak \u00e7arpmalar, toplamaya \u00e7evrilir. Mesela; 150 ile 254\u2019\u00fc \u00e7arpmak i\u00e7in, iki say\u0131n\u0131n logaritmalar\u0131 tablodan bulunur ve toplan\u0131r. Sonra bu logaritmaya kar\u015f\u0131 gelen say\u0131 tablodan aran\u0131r ki, bulunan sonu\u00e7, s\u00f6zkonusu iki say\u0131n\u0131n \u00e7arp\u0131m\u0131ndan ibarettir. 150 ve 254\u2019\u00fcn logaritmalar\u0131 s\u0131ra ile 2,17661 ve 2,4048\u2019dir. Toplam 4,5809 olur. Logaritmas\u0131 bu olan say\u0131 aran\u0131rsa, 38100 bulunur.<\/p>\n

E\u011fer taban olarak yakla\u015f\u0131k 2,71828 olan \u201ce\u201d say\u0131s\u0131 al\u0131n\u0131rsa, bu logaritma tabii logaritma veya ke\u015ffeden John Napier\u2019e izafeten Napier logaritmas\u0131 olarak da isimlendirilir.<\/p>\n

Adi ve Do\u011fal logaritmalar birbirleri ile ilgili olup, do\u011fal logaritma, basit logaritmaya 0,4343 say\u0131s\u0131 ile \u00e7arparak \u00e7evrilebilir. Basit ve do\u011fal logaritmalar\u0131n d\u0131\u015f\u0131nda herhangi pozitif bir reel say\u0131 taban\u0131na g\u00f6re de logaritma kullan\u0131l\u0131r. Ancak negatif say\u0131lar\u0131n hi\u00e7bir tabana g\u00f6re logaritmas\u0131n\u0131n olmayaca\u011f\u0131 a\u00e7\u0131kt\u0131r.<\/p>\n","protected":false},"excerpt":{"rendered":"

Logaritma on yedinci y\u00fczy\u0131l\u0131n ba\u015f\u0131nda hesaplar\u0131 h\u0131zland\u0131rmak i\u00e7in ke\u015ffedilen bir matematik y\u00f6ntemidir. Logaritma 300 y\u0131ldan daha uzun bir zaman boyunca temel bir hesap metodu olmu\u015ftur. On dokuzuncu y\u00fczy\u0131lda masa hesap…<\/p>\n","protected":false},"author":1,"featured_media":10368,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[1642,1643,1645,1644,1641],"class_list":["post-3287","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-egitim","tag-basit-logaritma","tag-dogal-logaritma","tag-john-napier","tag-joost-burgi","tag-logaritma"],"_links":{"self":[{"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/posts\/3287"}],"collection":[{"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3287"}],"version-history":[{"count":13,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/posts\/3287\/revisions"}],"predecessor-version":[{"id":12005,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/posts\/3287\/revisions\/12005"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/media\/10368"}],"wp:attachment":[{"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3287"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3287"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3287"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}