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Matematik yeni müfredata uygun AYT Matematik Logaritma konu anlatım ve soru çözümleri yaptığımız dersimizde logartma dan önce üstel fonksiyon nedir onu tanımlıyoruz. Üstel fonksiyonların...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3445373/a90757095b531c6c0bf5c18176fd7836/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/AhMsOAEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"10","reqid":"1769473546512240-5871364296597654084-balancer-l7leveler-kubr-yp-vla-255-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769473546512240-5871364296597654084-balancer-l7leveler-kubr-yp-vla-255-BAL&text=videoid:11273849774564645266","teaser":[{"list":{"type":"unordered","items":["Bu video, Mehmet Hoca tarafından sunulan bir matematik eğitim içeriğidir. Öğretmen, logaritma konusunu adım adım anlatmaktadır.","Video, logaritma serisinin ilk bölümü olup, öncelikle üslü sayılar tekrar edilmekte, ardından üstel fonksiyonların tanımı ve özellikleri ele alınmaktadır. Öğretmen, a değerinin 1'den büyük veya küçük olması durumunda fonksiyonun artan veya azalan olduğunu açıklamakta ve bu fonksiyonların grafiklerini çizerek yorumlamaktadır.","Videoda üstel fonksiyonların temel kuralları, artan ve azalan fonksiyonların nasıl tanımlanacağı ve grafiklerinin nasıl çizileceği örneklerle gösterilmektedir. Video, logaritma fonksiyonunun ikinci derste anlatılacağı bilgisiyle sonlanmaktadır."]},"endTime":1403,"title":"Logaritma ve Üstel Fonksiyonlar Matematik Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Logaritma Dersine Giriş","list":{"type":"unordered","items":["Mehmet hocanın logaritma konusunda detaylı notlar sunacağı belirtiliyor.","Öğrencilerden dersleri izlerken aktif olmaları, not alıp çözümleri kendilerinin yapmaları isteniyor.","Logaritma konusunu temelden zirveye çıkacak şekilde anlatacaklar."]},"beginTime":0,"endTime":77,"href":"/video/preview/11273849774564645266?parent-reqid=1769473546512240-5871364296597654084-balancer-l7leveler-kubr-yp-vla-255-BAL&text=RodriR12&t=0&ask_summarization=1"},{"index":1,"title":"Üslü Sayılar Tekrarı","list":{"type":"unordered","items":["Logaritmayı anlayabilmek için önce üstel fonksiyonu, üstel fonksiyonu ise üslü sayıları bilmek gerekiyor.","Üslü ifadelerde a^n = a×a×...×a (n tane a) şeklinde gösterilir.","Üslü sayılarla ilgili temel kurallar: a^x × a^y = a^(x+y), (a^x)^y = a^(x×y), a^x / a^y = a^(x-y), a^1 = a."]},"beginTime":77,"endTime":175,"href":"/video/preview/11273849774564645266?parent-reqid=1769473546512240-5871364296597654084-balancer-l7leveler-kubr-yp-vla-255-BAL&text=RodriR12&t=77&ask_summarization=1"},{"index":2,"title":"Üslü Sayılar ve Köklü Sayılar","list":{"type":"unordered","items":["Her köklü sayı bir üslü sayıdır: n√(a^x) = a^(x/n).","Üslü sayılarla ilgili bir örnek soru çözülüyor.","Üslü sayılar konusunu hatırladıktan sonra logaritma konusuna geçiliyor."]},"beginTime":175,"endTime":301,"href":"/video/preview/11273849774564645266?parent-reqid=1769473546512240-5871364296597654084-balancer-l7leveler-kubr-yp-vla-255-BAL&text=RodriR12&t=175&ask_summarization=1"},{"index":3,"title":"Üstel Fonksiyon Tanımı","list":{"type":"unordered","items":["Üstel fonksiyon tanımı: a ∈ R+ ve a ≠ 1 olmak üzere, f: R → R+ ve f(x) = a^x şeklinde tanımlanan fonksiyonlardır.","Üstel fonksiyonlarda a değeri pozitif reel sayı olmalı ve 1 olmamalıdır.","f(x) = 2^x, f(x) = 5^x, f(x) = 3^x+1 üstel fonksiyonlardır, f(x) = (-3)^x ve f(x) = 1^x üstel fonksiyon değildir.","1'in bütün kuvvetleri 1 olduğu için f(x) = 1^x ifadesi üstel fonksiyon olarak alınmaz."]},"beginTime":301,"endTime":493,"href":"/video/preview/11273849774564645266?parent-reqid=1769473546512240-5871364296597654084-balancer-l7leveler-kubr-yp-vla-255-BAL&text=RodriR12&t=301&ask_summarization=1"},{"index":4,"title":"Üstel Fonksiyonların Tanımı ve Özellikleri","list":{"type":"unordered","items":["Üstel fonksiyon tanımı: a üzeri x şeklindeki fonksiyonlarda a değeri pozitif reel sayı olmalı ve 1'e eşit olmamalıdır.","Üstel fonksiyonun en geniş değer aralığı, a'nın 0'dan büyük ve 1'e eşit olmayan değerleridir.","Üstel fonksiyonun tanım aralığı tüm reel sayılar, değer aralığı ise 0'dan büyük tüm reel sayılar olur."]},"beginTime":502,"endTime":637,"href":"/video/preview/11273849774564645266?parent-reqid=1769473546512240-5871364296597654084-balancer-l7leveler-kubr-yp-vla-255-BAL&text=RodriR12&t=502&ask_summarization=1"},{"index":5,"title":"Artan ve Azalan Fonksiyonlar","list":{"type":"unordered","items":["a üzeri x fonksiyonunda a değeri 1'den büyükse fonksiyon artandır ve grafiği yukarı doğru eğilimlidir.","a üzeri x fonksiyonunda a değeri 0 ile 1 arasında ise fonksiyon azalandır ve grafiği aşağı doğru eğilimlidir.","Artan fonksiyonda x değeri arttıkça fonksiyon değeri de artar, azalan fonksiyonda ise x değeri arttıkça fonksiyon değeri azalır."]},"beginTime":637,"endTime":841,"href":"/video/preview/11273849774564645266?parent-reqid=1769473546512240-5871364296597654084-balancer-l7leveler-kubr-yp-vla-255-BAL&text=RodriR12&t=637&ask_summarization=1"},{"index":6,"title":"Üstel Fonksiyonların Grafikleri","list":{"type":"unordered","items":["Üstel fonksiyonların grafiklerini çizmek için x değerlerine göre y değerlerini hesaplayıp noktaları işaretleyebiliriz.","Artan üstel fonksiyonların grafikleri yukarı doğru eğilimli, azalan üstel fonksiyonların grafikleri ise aşağı doğru eğilimlidir.","Üstel fonksiyonların tabanı arttıkça (a değeri arttıkça) grafiği y eksenine daha yakın olur."]},"beginTime":841,"endTime":1110,"href":"/video/preview/11273849774564645266?parent-reqid=1769473546512240-5871364296597654084-balancer-l7leveler-kubr-yp-vla-255-BAL&text=RodriR12&t=841&ask_summarization=1"},{"index":7,"title":"Üstel Fonksiyon Problemi Çözümü","list":{"type":"unordered","items":["Verilen g(x) fonksiyonunun grafiğine göre g(2) değeri bulunması isteniyor.","g(x) fonksiyonu artan ve üstel bir fonksiyon olduğu belirleniyor, a^x veya a^x+b şeklinde ifade edilebilir.","Verilen noktalar kullanılarak g(x) = (5/3)^x - 2 şeklinde üstel fonksiyonun denklemi 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