b = ax ifadesinde x de\u011ferini bulma i\u015flemine logaritma denir.
\n ax = b ise x= logab dir.<\/p>\n
\u00d6rnekler:<\/p>\n
log3x = 5 ise x = 35 = 243’t\u00fcr.
\n log6216 = x ise x = 3 bulunur.<\/p>\n
Logaritma Fonksiyonunun \u00d6zellikleri<\/p>\n
loga(m.n) = logam + logan dir.
\n (\u00c7arp\u0131m\u0131n logaritmas\u0131, \u00e7arpanlar\u0131n logaritmalar\u0131n\u0131n toplam\u0131na e\u015fittir.)<\/p>\n
loga(m \/ n) = logam – logan dir.
\n (B\u00f6l\u00fcm\u00fcn logaritmas\u0131, pay\u0131n logaritmas\u0131ndan paydan\u0131n logaritmas\u0131n\u0131n fark\u0131na e\u015fittir.)<\/p>\n
loga1 = 0.
\n (1 say\u0131s\u0131n\u0131n her tabandaki logaritmas\u0131, a0=1 e\u015fitli\u011finden dolay\u0131 s\u0131f\u0131rd\u0131r.)<\/p>\n
logaa = 1
\n (Taban\u0131n logaritmas\u0131, a1=a e\u015fitli\u011finden dolay\u0131 1 dir.)<\/p>\n
logapn = n.logap<\/p>\n
logap = logcp \/ logca d\u0131r.
\n (Taban De\u011fi\u015ftirme Kural\u0131)<\/p>\n
alogap = p<\/p>\n
\u00d6rnekler:<\/p>\n
log(2x + 12) = 1 + log(x – 2) denklemini sa\u011flayan x de\u011feri nedir?<\/p>\n
log(2x + 12) = log10 + log(x – 2)
\n log(2x + 12) = log[10.(x – 2)]
\n 2x + 12 = 10x – 20
\n x = 4 bulunur.<\/p>\n
(log2x)2 – 6log2x + 8 = 0 denkleminin \u00e7\u00f6z\u00fcm k\u00fcmesi nedir?<\/p>\n
log2x = t diyelim.
\n t2 – 6t + 8 = 0 olur.
\n Bu denklemin k\u00f6kleri t1 = 2 ve t2 = 4 t\u00fcr.
\n Buradan log2x = 2 veya log2x = 4 olur.
\n O halde x de\u011ferleri 22 = 4 ve 24 = 16 olup
\n \u00c7.K = {4,16} bulunur.<\/p>\n","protected":false},"excerpt":{"rendered":"
b = ax ifadesinde x de\u011ferini bulma i\u015flemine logaritma denir. ax = b ise x= logab dir. \u00d6rnekler: log3x = 5 ise x = 35 = 243’t\u00fcr. log6216 = x ise x = 3 bulunur. Logaritma Fonksiyonunun \u00d6zellikleri loga(m.n) = logam + logan dir. (\u00c7arp\u0131m\u0131n logaritmas\u0131, \u00e7arpanlar\u0131n logaritmalar\u0131n\u0131n toplam\u0131na e\u015fittir.) loga(m \/ n) = logam …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1404,1403],"tags":[7232,7233],"class_list":["post-3046","post","type-post","status-publish","format-standard","hentry","category-matematik-odevleri","category-odevler","tag-logaritma","tag-logaritma-fonksiyonunun-ozellikleri"],"_links":{"self":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3046","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/comments?post=3046"}],"version-history":[{"count":0,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3046\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/media?parent=3046"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/categories?post=3046"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/tags?post=3046"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}