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Eğitmen, Logi kitabından örnekler çözerek konuyu açıklamaktadır.","Video, üstel fonksiyonların tanımı ve özellikleriyle başlayıp, logaritma fonksiyonlarının tanımı, özellikleri ve çözüm yöntemlerine geçmektedir. İçerikte basit ve bileşik kesir üstel fonksiyonlar, logaritma fonksiyonlarının tanım kümesi, doğal logaritma (ln) ve logaritma özellikleri detaylı şekilde anlatılmaktadır.","Eğitmen, logaritma fonksiyonlarında x'i yalnız bırakmak için logaritma tabanını kullanma, ters fonksiyon bulma ve logaritma fonksiyonlarının tanım kümesi için gerekli koşulları (taban ve iç fonksiyonun pozitif olması, tabanın 1'e eşit olmaması) açıklamaktadır. Video boyunca çeşitli örnek sorular çözülerek konu pekiştirilmektedir."]},"endTime":1694,"title":"Üstel ve Logaritma Fonksiyonları Matematik Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Üstel Fonksiyon Tanımı","list":{"type":"unordered","items":["Üstel fonksiyon, tabanı pozitif bir reel sayı olan ve üstünde değişken olan denklemdir.","Üstel fonksiyonlarda taban kesinlikle negatif olmamalı ve 1'e eşit olmamalıdır.","Üstel fonksiyonlar iki türdür: basit kesir (0-1 arası) ve bileşik kesir (1'den büyük)."]},"beginTime":0,"endTime":70,"href":"/video/preview/13796912975944603916?parent-reqid=1767349407753900-12435982791918238585-balancer-l7leveler-kubr-yp-klg-70-BAL&text=eMe+Logar&t=0&ask_summarization=1"},{"index":1,"title":"Basit Kesir Üstel Fonksiyonlar","list":{"type":"unordered","items":["Taban 0-1 arasındaysa (basit kesir) üstel fonksiyon azalan fonksiyondur.","Basit kesir üstel fonksiyonların grafiği sola doğru gittikçe artar, sağa doğru gittikçe azalır ve hiçbir zaman sıfıra ulaşamaz.","Herhangi bir pozitif sayının kuvveti negatif çıkamaz."]},"beginTime":70,"endTime":143,"href":"/video/preview/13796912975944603916?parent-reqid=1767349407753900-12435982791918238585-balancer-l7leveler-kubr-yp-klg-70-BAL&text=eMe+Logar&t=70&ask_summarization=1"},{"index":2,"title":"Bileşik Kesir Üstel Fonksiyonlar","list":{"type":"unordered","items":["Taban 1'den büyükse (bileşik kesir) üstel fonksiyon daima artandır.","Bileşik kesir üstel fonksiyonların grafiği hiçbir zaman sıfıra değmez, sıfırıncı kuvveti 1'dir ve devamında artar.","Herhangi bir pozitif sayının kuvveti negatif çıkamaz."]},"beginTime":143,"endTime":194,"href":"/video/preview/13796912975944603916?parent-reqid=1767349407753900-12435982791918238585-balancer-l7leveler-kubr-yp-klg-70-BAL&text=eMe+Logar&t=143&ask_summarization=1"},{"index":3,"title":"Üstel Fonksiyon Örnekleri","list":{"type":"unordered","items":["Azalan üstel fonksiyonların görüntü kümesi, uç değerlerle belirlenir.","Üstel fonksiyonların grafiği verildiğinde, fonksiyonun değerleri hesaplanabilir.","Üstel fonksiyonların tersi logaritma fonksiyonudur."]},"beginTime":194,"endTime":474,"href":"/video/preview/13796912975944603916?parent-reqid=1767349407753900-12435982791918238585-balancer-l7leveler-kubr-yp-klg-70-BAL&text=eMe+Logar&t=194&ask_summarization=1"},{"index":4,"title":"Logaritma Özellikleri","list":{"type":"unordered","items":["Logaritmada taban negatif olamaz ve 1'e eşit olamaz.","Logaritma fonksiyonunun içi her zaman pozitif olmalıdır.","Logaritma fonksiyonunda taban ve içi negatif olamaz."]},"beginTime":474,"endTime":557,"href":"/video/preview/13796912975944603916?parent-reqid=1767349407753900-12435982791918238585-balancer-l7leveler-kubr-yp-klg-70-BAL&text=eMe+Logar&t=474&ask_summarization=1"},{"index":5,"title":"Logaritma ve Fonksiyon Örneği","list":{"type":"unordered","items":["Logaritma fonksiyonlarında, logaritma tabanı öbür tarafa atıldığında üs olarak geçer.","Fonksiyonların tersi, fonksiyonun tersini bulmak için x'i yalnız bırakmak gerekir.","Logaritma fonksiyonlarında, logaritma tabanı ve içi arasındaki ilişki kullanılarak denklemler çözülebilir."]},"beginTime":557,"endTime":704,"href":"/video/preview/13796912975944603916?parent-reqid=1767349407753900-12435982791918238585-balancer-l7leveler-kubr-yp-klg-70-BAL&text=eMe+Logar&t=557&ask_summarization=1"},{"index":6,"title":"Üstel Fonksiyonlar ve Logaritma","list":{"type":"unordered","items":["Üstel fonksiyonlarda x'i bulmak için önce x'leri bir araya getirmek gerekir.","a üzeri x = y ise x'i yalnız bırakmak için loga olarak at, loga x = y ise x'i bulmak için a olarak at.","Üstel fonksiyon sorularında, üsleri aynıysa tabanlar bölünür."]},"beginTime":708,"endTime":797,"href":"/video/preview/13796912975944603916?parent-reqid=1767349407753900-12435982791918238585-balancer-l7leveler-kubr-yp-klg-70-BAL&text=eMe+Logar&t=708&ask_summarization=1"},{"index":7,"title":"Üstel Fonksiyon Örnekleri","list":{"type":"unordered","items":["Üstel fonksiyon sorularında, üsleri aynı olan ifadeleri bir değişkene atayarak denklem çözülebilir.","Üstel fonksiyon sorularında, üsleri aynı olan ifadeleri bir değişkene atayarak denklem çözülebilir.","Üstel fonksiyon sorularında, üsleri aynı olan ifadeleri bir değişkene atayarak denklem çözülebilir."]},"beginTime":797,"endTime":951,"href":"/video/preview/13796912975944603916?parent-reqid=1767349407753900-12435982791918238585-balancer-l7leveler-kubr-yp-klg-70-BAL&text=eMe+Logar&t=797&ask_summarization=1"},{"index":8,"title":"Logaritma Sıralama Sorusu","list":{"type":"unordered","items":["Logaritma sorularında, üslerin değerlerini karşılaştırarak sıralama yapılabilir.","Üslerin değerlerini karşılaştırarak sıralama yapılabilir.","Üslerin değerlerini karşılaştırarak sıralama yapılabilir."]},"beginTime":951,"endTime":1048,"href":"/video/preview/13796912975944603916?parent-reqid=1767349407753900-12435982791918238585-balancer-l7leveler-kubr-yp-klg-70-BAL&text=eMe+Logar&t=951&ask_summarization=1"},{"index":9,"title":"Ters Fonksiyonlar","list":{"type":"unordered","items":["Ters fonksiyonu bulurken x'i yalnız bırakmak gerekir.","Logaritma ve üstel fonksiyon bilgisi sayesinde ters fonksiyonlar rahatlıkla bulunabilir.","Ters fonksiyonlar konusu, fonksiyonlar oynatma listesinden bulunabilir."]},"beginTime":1048,"endTime":1132,"href":"/video/preview/13796912975944603916?parent-reqid=1767349407753900-12435982791918238585-balancer-l7leveler-kubr-yp-klg-70-BAL&text=eMe+Logar&t=1048&ask_summarization=1"},{"index":10,"title":"Fonksiyon Yorumları","list":{"type":"unordered","items":["Fonksiyon yorumlarında, f(g(x)) = 2x şeklinde verilen ifadelerde, g(x) yerine log2(x) yazılabilir.","Fonksiyon yorumlarında, x gördüğümüz yere x yapmak için uygun bir sayı yazılmalıdır.","Ters fonksiyon bilgisi, fonksiyon yorumlarında önemli bir rol oynar."]},"beginTime":1132,"endTime":1216,"href":"/video/preview/13796912975944603916?parent-reqid=1767349407753900-12435982791918238585-balancer-l7leveler-kubr-yp-klg-70-BAL&text=eMe+Logar&t=1132&ask_summarization=1"},{"index":11,"title":"Logaritma Fonksiyonlarının Tanım Kümesi","list":{"type":"unordered","items":["Logaritma fonksiyonunun içi her zaman pozitiftir.","Logaritma tabanı her zaman pozitiftir ve 1'e eşit olamaz.","Logaritma fonksiyonunun tanım kümesi, iç ifadenin pozitif olması koşuluyla belirlenir."]},"beginTime":1216,"endTime":1407,"href":"/video/preview/13796912975944603916?parent-reqid=1767349407753900-12435982791918238585-balancer-l7leveler-kubr-yp-klg-70-BAL&text=eMe+Logar&t=1216&ask_summarization=1"},{"index":12,"title":"Logaritma Özellikleri","list":{"type":"unordered","items":["Logaritma e tabanında x, doğal logaritma olarak adlandırılır ve yaklaşık 2,718 değerine sahiptir.","Logaritma 10 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Öğretmen, logaritma kurallarını uygulayarak soruyu adım adım çözmekte ve altın oranın karesinin altın oran ile birim toplamına eşit olduğunu göstermektedir. 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İlk bölümde üstel fonksiyonun özellikleri ve logaritma fonksiyonunun temel özellikleri (logaritma a tabanında 1 = 0, logaritma a tabanında a = 1, logaritma a tabanında x çarpı y = logaritma a tabanında x + logaritma a tabanında y vb.) açıklanırken, ikinci bölümde logaritma taban değiştirme kuralı ve logaritma özellikleri (çarpma, bölme, üslü ifadeler) örneklerle anlatılmaktadır.","Video boyunca çeşitli örnekler çözülerek logaritma problemlerinin nasıl çözüleceği adım adım gösterilmekte ve video sonunda izleyicilerin daha fazla soru çözmesi gerektiği vurgulanmaktadır."]},"endTime":1248,"title":"Logaritma Konusu Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Üstel Fonksiyon","list":{"type":"unordered","items":["Üstel fonksiyon, a ∈ R+ (1≠) ve x ∈ R olmak üzere f: R → R+ tanımlı f(x) = a^x biçimindeki fonksiyonlardır.","a sayısı üstel fonksiyonun tabanı, x sayısı ise fonksiyonun değişkeni olarak adlandırılır.","a > 1 olduğunda fonksiyon artan, 0,1 \u003c a \u003c 1 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