Logaritma<\/p>\n
\u00dcstel fonksiyon<\/p>\n
a ger\u00e7ek say\u0131, n pozitif tam say\u0131 ise, an = a.a.a. \u2026 . a d\u0131r.<\/p>\n
an say\u0131s\u0131nda \u00fcsl\u00fc say\u0131, a ya taban , n ye \u00fcs denir.
\nan say\u0131s\u0131, “a \u00fcss\u00fc n” diye okunur.<\/p>\n
1. n \uf0cez+ ise an \uf03da.a . \u2026 a,
\n2. n \uf0cez- ise an \uf03d 1\uf02fa-n ,
\n3. n \uf03d 0 ise an\uf03d a0 \uf03d 1 \uf028a \uf0b9 0\uf029,
\n4. n \uf0cez+ ise a1\/ n \uf03d x \uf0db a \uf03d xn ,
\n5. m\/n \uf0ce q ise am\/n \uf03d \uf028 a1\/n \uf029m dir.<\/p>\n
S\u0131f\u0131rdan farkl\u0131 a ger\u00e7ek say\u0131s\u0131 i\u00e7in, a0 \uf03d 1 dir.<\/p>\n
2-5 , 2-3 , 20 , 22\/3 ger\u00e7ek say\u0131lar\u0131, \u00fcstl\u00fc ger\u00e7ek say\u0131lard\u0131r.
\nPozitif a ger\u00e7ek say\u0131s\u0131 i\u00e7in, \u00fcstleri irasyonel say\u0131 olan a\uf0d62 , a-\uf0d62 , a\uf070 gibi say\u0131lar da \u00fcsl\u00fc ger\u00e7ek say\u0131lard\u0131r.
\nPozitif bir ger\u00e7ek say\u0131n\u0131n rasyonel kuvvetleri birer ger\u00e7ek say\u0131d\u0131r. Bu say\u0131lar\u0131n \u00e7arp\u0131m\u0131 ve b\u00f6l\u00fcm\u00fcne
\nait \u00f6zellikleri biliyoruz a, 1 den farkl\u0131 pozitif ger\u00e7ek say\u0131, x say\u0131s\u0131n\u0131n g\u00f6r\u00fcnt\u00fcs\u00fcn\u00fcn ax \u00fcstl\u00fc say\u0131s\u0131 oldugunu belirten fonksiyonu tan\u0131mlad\u0131m.<\/p>\n
tan\u0131m
\na \uf0ceIR+ ve a \uf0b9 1 olmak \u00fczere, f : IR \uf0ae IR+, f(x) = ax bi\u00e7iminde tan\u0131mlanan f fonksiyonuna, \u00fcstel fonksiyon denir.<\/p>\n
f \u00fcstel fonksiyonuna g\u00f6re, x ger\u00e7ek say\u0131s\u0131n\u0131n (degi\u015fkenin) g\u00f6r\u00fcnt\u00fcs\u00fc, ax \u00fcsl\u00fc ger\u00e7ek say\u0131s\u0131d\u0131r.
\na pozitif ger\u00e7ek say\u0131 oldu\u011fundan, her x ger\u00e7ek say\u0131s\u0131 i\u00e7in f (x)= ax > 0 d\u0131r.<\/p>\n
\u00d6rnek
\nf(x)= 2x ile tan\u0131ml\u0131, f: IR \uf0ae IR+ \u00fcstel fonksiyonu veriliyor.
\nf(1), f (1\/2), f(-1), f(0), f(-3) degerlerini bulal\u0131m
\n\u00c7\u00f6z\u00fcm
\nf(x) = 2x \uf0ae f(1)=21=2, f(1\/2)=21\/2 =\uf0d62 \uf0bb 1,41 \u2026 , f(-1)=2-1=1\/2, f(0)=20=1, f(-3)=2-3=1\/23=1\/8 bulunur.<\/p>\n
\u00dcstel fonksiyon, \u00fcsl\u00fc ifadelerde g\u00f6rd\u00fc\u011f\u00fcm\u00fcz b\u00fct\u00fcn \u00f6zellikleri IR \u00fczerinde sa\u011flar.
\na,b \uf0ce IR+ , a\uf0b91, b\uf0b91 ve x,y\uf0ce IR i\u00e7in a\u015fa\u011f\u0131daki \u00f6zellikler vard\u0131r:<\/p>\n
1. ax.ay=ax+y, 2. (ax)y=ax.y, 3. (a.b)x=ax.bx, 4.ax\/ay=ax-y,<\/p>\n
5.(a\/b)x=ax\/bx , 6.ax\/ay=1\/ay-x, 7. a0=1, 8. (1\/a)x=a-x<\/p>\n
9.a\uf0ceIR+ ve a\uf0b91 olmak \u00fczere, ax…<\/p>\n","protected":false},"excerpt":{"rendered":"
Logaritma \u00dcstel fonksiyon a ger\u00e7ek say\u0131, n pozitif tam say\u0131 ise, an = a.a.a. \u2026 . a d\u0131r. an say\u0131s\u0131nda \u00fcsl\u00fc say\u0131, a ya taban , n ye \u00fcs denir. an say\u0131s\u0131, “a \u00fcss\u00fc n” diye okunur. 1. n \uf0cez+ ise an \uf03da.a . \u2026 a, 2. n \uf0cez- ise an \uf03d 1\uf02fa-n , 3. …<\/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":[7232,7368],"class_list":["post-3150","post","type-post","status-publish","format-standard","hentry","category-matematik-odevleri","category-odevler","tag-logaritma","tag-ustel-fonksiyon"],"_links":{"self":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3150","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=3150"}],"version-history":[{"count":0,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3150\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/media?parent=3150"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/categories?post=3150"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/tags?post=3150"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}