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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=1770076237157297-9632834681340769426-balancer-l7leveler-kubr-yp-vla-45-BAL&text=easymathk12&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=1770076237157297-9632834681340769426-balancer-l7leveler-kubr-yp-vla-45-BAL&text=easymathk12&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=1770076237157297-9632834681340769426-balancer-l7leveler-kubr-yp-vla-45-BAL&text=easymathk12&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=1770076237157297-9632834681340769426-balancer-l7leveler-kubr-yp-vla-45-BAL&text=easymathk12&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=1770076237157297-9632834681340769426-balancer-l7leveler-kubr-yp-vla-45-BAL&text=easymathk12&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=1770076237157297-9632834681340769426-balancer-l7leveler-kubr-yp-vla-45-BAL&text=easymathk12&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=1770076237157297-9632834681340769426-balancer-l7leveler-kubr-yp-vla-45-BAL&text=easymathk12&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 bulunuyor."]},"beginTime":1113,"endTime":1237,"href":"/video/preview/11273849774564645266?parent-reqid=1770076237157297-9632834681340769426-balancer-l7leveler-kubr-yp-vla-45-BAL&text=easymathk12&t=1113&ask_summarization=1"},{"index":8,"title":"Fonksiyon Değerinin Hesaplanması","list":{"type":"unordered","items":["g(2) değeri için x yerine 2 yazarak (5/3)^2 - 2 = 19/9 olarak hesaplanıyor.","Benzer bir problemde f(x) = a^x fonksiyonu için f(1) = 2/5 değerinden a = 2/5 bulunuyor.","f(2) ve f(-1) değerleri hesaplanarak f(2)·f(-1) = 2/5 olarak bulunuyor."]},"beginTime":1237,"endTime":1378,"href":"/video/preview/11273849774564645266?parent-reqid=1770076237157297-9632834681340769426-balancer-l7leveler-kubr-yp-vla-45-BAL&text=easymathk12&t=1237&ask_summarization=1"},{"index":9,"title":"Dersin Sonu ve Öneriler","list":{"type":"unordered","items":["İlk derste üstel fonksiyonun tanımı ve mantığı anlatılmıştır.","İkinci derste logaritma fonksiyonunun tanımı yapılacaktır.","Öğrencilere dersi tekrar etmeleri, dinlenmeleri ve logaritma konusuna geçmeden çalışmaları tavsiye ediliyor."]},"beginTime":1378,"endTime":1402,"href":"/video/preview/11273849774564645266?parent-reqid=1770076237157297-9632834681340769426-balancer-l7leveler-kubr-yp-vla-45-BAL&text=easymathk12&t=1378&ask_summarization=1"}],"linkTemplate":"/video/preview/11273849774564645266?parent-reqid=1770076237157297-9632834681340769426-balancer-l7leveler-kubr-yp-vla-45-BAL&text=easymathk12&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Logaritma 1 | 12.Sınıf Matematik (yeni müfredat) | AYT Matematik #12.sınıf 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Tepkimeler","list":{"type":"unordered","items":["Kendiliğinden gerçekleşmeyip elektrik enerjisi ile gerçekleştirilebilen elektrokimyasal tepkimelere istemsiz tepkimeler veya elektroliz denir.","Elektrokimyasal pillerde iletken telin bağlı olduğu metal çubuklara elektrot, elektrotların batırıldığı iletken çözeltilere ise elektrolit denir.","Standart indirgenme potansiyeli negatif metallere aktif metal denir."]},"beginTime":138,"endTime":236,"href":"/video/preview/8826782451222558824?parent-reqid=1770076237157297-9632834681340769426-balancer-l7leveler-kubr-yp-vla-45-BAL&text=easymathk12&t=138&ask_summarization=1"},{"index":3,"title":"Elektrokimyasal Pil ve Korozyon","list":{"type":"unordered","items":["Çalışmakta olan bir elektrokimyasal pilde yarı hücrede elektronik değişimi zamanla azalırsa, bu indirgenme olan katot yarı hücresi olur.","Metallerin zamanla dış etkilerden dolayı paslanma ve yıpranmasına korozyon denir."]},"beginTime":236,"endTime":275,"href":"/video/preview/8826782451222558824?parent-reqid=1770076237157297-9632834681340769426-balancer-l7leveler-kubr-yp-vla-45-BAL&text=easymathk12&t=236&ask_summarization=1"},{"index":4,"title":"Eşleştirme Soruları","list":{"type":"unordered","items":["Oksijenin flor ile oluşturduğu bileşiklerde oksijen artı iki değerli kalır çünkü flor daha elektronegatif olup eksi bir değerli kalır.","Hidrojen metallerle oluşturduğu bileşikteki yükseltgenme basamağı eksi bir değerlidir.","Yükseltgenme olayının gerçekleştiği yarı hücreye anot denir."]},"beginTime":275,"endTime":356,"href":"/video/preview/8826782451222558824?parent-reqid=1770076237157297-9632834681340769426-balancer-l7leveler-kubr-yp-vla-45-BAL&text=easymathk12&t=275&ask_summarization=1"},{"index":5,"title":"Tuz Köprüsü ve Elektroliz","list":{"type":"unordered","items":["Tuz köprüsünde katyonların taşındığı yer katot hücredir çünkü katonda katyon azalır ve tuz köprüsü katyon 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anlatılan yöntemle sorular çözülecek.","Redoks denkleştirmede ilk adım elektron alışverişi yapan maddeleri tespit etmektir.","Serbest radika atomlar ve sülfat köklerindeki S atomları elektron alışverişi yapar."]},"beginTime":659,"endTime":691,"href":"/video/preview/8826782451222558824?parent-reqid=1770076237157297-9632834681340769426-balancer-l7leveler-kubr-yp-vla-45-BAL&text=easymathk12&t=659&ask_summarization=1"},{"index":8,"title":"Redoks Denkleştirme Adımları","list":{"type":"unordered","items":["Redoks denkleştirme sırasında yük değişimlerini bulmak gerekir.","Sülfat köklerindeki S atomları her zaman +6 yük değerine sahiptir.","Elektron sayıları eşitlenmesi için denklemin her iki tarafı da çarpılmalıdır."]},"beginTime":691,"endTime":817,"href":"/video/preview/8826782451222558824?parent-reqid=1770076237157297-9632834681340769426-balancer-l7leveler-kubr-yp-vla-45-BAL&text=easymathk12&t=691&ask_summarization=1"},{"index":9,"title":"Tepkime 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