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Öğretmen, video sonunda daha fazla soru çözümü için gelecek bir kayıt yapacağını belirtmektedir."]},"endTime":1765,"title":"Matematik Dersi: Logaritma ve Fonksiyonlar","beginTime":0}],"fullResult":[{"index":0,"title":"Giriş ve Logaritma Videoları Hakkında Bilgilendirme","list":{"type":"unordered","items":["Eğitmen, Endemik Yayınlarından gelen yenilenmiş AYT matematik soru bankasından logaritma konusunu ele alacak.","Kanalda beş saate yakın logaritma videosu bulunmakta, bunların beşi grafik, üçü tanım konusunu içermektedir.","Bu videoda temel ve orta düzey logaritma soruları çözülecek, konuyu iyi bildiğinizi düşünenler yeni nesil soru çözümlerini beklemeleri önerilmektedir."]},"beginTime":0,"endTime":123,"href":"/video/preview/2933767120302784548?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=0&ask_summarization=1"},{"index":1,"title":"İlk Logaritma Sorusu","list":{"type":"unordered","items":["İlk soruda logaritma kök iki tabanında dokuz ifadesi çözülmektedir.","Kök iki ifadesi 2 üzeri 1/2 olarak, dokuz ise 3 üzeri 2 olarak yazılabilir.","Logaritma özellikleri kullanılarak ifade sadeleştirilerek sonucun 4/3 olduğu bulunmuştur."]},"beginTime":123,"endTime":251,"href":"/video/preview/2933767120302784548?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=123&ask_summarization=1"},{"index":2,"title":"İkinci Logaritma Sorusu","list":{"type":"unordered","items":["İkinci soruda karekök ve küpkök içeren karmaşık bir logaritma ifadesi çözülmektedir.","Kök ifadeleri ve tabanlar aynı temel sayıya (2) indirgenerek sadeleştirme yapılmıştır.","Sonuç olarak logaritma 2 tabanında 2 üzeri 19/24 ifadesi elde edilmiş ve cevap 19/24 olarak bulunmuştur."]},"beginTime":251,"endTime":377,"href":"/video/preview/2933767120302784548?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=251&ask_summarization=1"},{"index":3,"title":"Üçüncü Soru - Fonksiyonun Tanım Kümesi","list":{"type":"unordered","items":["Üçüncü soruda logaritma fonksiyonunun en geniş tanım kümesinde kaç doğal sayı olduğunu bulmak istenmektedir.","Logaritma fonksiyonunun tanım koşulları: tabanın pozitif ve 1'den farklı olması, logaritmanın içindeki ifadenin sıfırdan büyük olması.","Verilen ifade çarpanlara ayrılarak x²-4x-21=(x-7)(x+3) şeklinde yazılmış ve x\u003c14, x≠13 koşulları belirlenmiştir."]},"beginTime":377,"endTime":428,"href":"/video/preview/2933767120302784548?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=377&ask_summarization=1"},{"index":4,"title":"Eşitsizlik Sorularında Tablo Oluşturma","list":{"type":"unordered","items":["Eşitsizlik sorularında (büyüktür, küçüktür gibi) kendinize güvenmeyin, mutlaka tablo oluşturun.","Kökleri görmezden gelip kaçırma riskini önlemek için tüm kökler için tablo oluşturun.","Köklerin işaretini değiştirdiği için (eksi ve artı) tabloda doğru işaretleri belirtin."]},"beginTime":432,"endTime":493,"href":"/video/preview/2933767120302784548?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=432&ask_summarization=1"},{"index":5,"title":"Eşitsizlik Çözümü","list":{"type":"unordered","items":["Çözüm kümesi, eşitsizliğin pozitif olduğu yerlerdir: eksi üç'ten sonsuza, yedi'den sonsuza kadar.","İki eşitsizliğin kesişimi, her iki eşitsizliği de sağlayan değerler kümesidir.","Çözüm kümesi: eksi sonsuzdan eksi üç'e ve yedi'den ondört'e kadar olan aralıklardır (onüç dahil değil)."]},"beginTime":493,"endTime":640,"href":"/video/preview/2933767120302784548?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=493&ask_summarization=1"},{"index":6,"title":"Logaritma Fonksiyonlarının Grafiği","list":{"type":"unordered","items":["Logaritma fonksiyonlarında, ifade sıfır olduğunda dikey asimptot oluşur.","Logaritma fonksiyonlarının tanım kümesinde sıfır bulunmaz, bu nedenle y eksenini çizmek gerekmez.","Logaritma fonksiyonlarının grafiği, sıfır olmayan değerler için çizilir ve sıfıra yaklaşınca dikey asimptot oluşur."]},"beginTime":640,"endTime":775,"href":"/video/preview/2933767120302784548?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=640&ask_summarization=1"},{"index":7,"title":"Logaritma Fonksiyonu Problemi","list":{"type":"unordered","items":["Verilen logaritma fonksiyonunda, x=-2 için fonksiyonun değeri c'dir.","Fonksiyonun sıfırdan geçtiği noktada, x=0 için a tabanında c değeri bulunur.","Verilen koşullar kullanılarak a=2, b=2 ve c=4 değerleri bulunur."]},"beginTime":775,"endTime":924,"href":"/video/preview/2933767120302784548?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=775&ask_summarization=1"},{"index":8,"title":"Logaritma Fonksiyonlarının Grafikleri","list":{"type":"unordered","items":["Tanım kümesi iki'den başlıyorsa, iki noktasında dikey asimptot oluşur ve değerler eksi sonsuzdan ikiye kadar olur.","Beş tabanında logaritma fonksiyonunun grafiği, üç noktayı birleştiren ve logaritma grafiğine benzeyen bir şekilde çizilir.","Mutlak değer işareti grafiğe eklendiğinde, negatif değerleri pozitif yaparak grafiği yukarı katlar ve sağ tarafta da değerler alabilir."]},"beginTime":930,"endTime":1041,"href":"/video/preview/2933767120302784548?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=930&ask_summarization=1"},{"index":9,"title":"Fonksiyonların Özellikleri","list":{"type":"unordered","items":["Grafikten yorum yaparak, x₁\u003cx₂ olduğunda f(x₁)>f(x₂) olduğu için fonksiyon azalandır.","Fonksiyon x ve y eksenlerini keser, birebir ve örten bir fonksiyondur.","Tanım kümesi tüm gerçek sayılar olduğunda, fonksiyon y ekseninin tamamını tarar ve birebir ve örten olur."]},"beginTime":1041,"endTime":1116,"href":"/video/preview/2933767120302784548?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=1041&ask_summarization=1"},{"index":10,"title":"Fonksiyon Tersi Hesaplama","list":{"type":"unordered","items":["e^(-15) = a eşitliğinde, her iki tarafın logaritması alınarak a değeri hesaplanır.","Fonksiyonun tersi hesaplanırken, x gördüğünüz yerde 1 yazılır ve fonksiyonla tersi birlikte kullanılır.","Ters fonksiyon hesaplanırken, tabanı 10 olan logaritma kullanılarak sonuç bulunur."]},"beginTime":1116,"endTime":1281,"href":"/video/preview/2933767120302784548?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=1116&ask_summarization=1"},{"index":11,"title":"Logaritma Sorusu Çözümü","list":{"type":"unordered","items":["Logaritma sorularında, logaritmanın içi sıfırdan büyük olmalı ve logaritma ifadesi sıfırdan büyük eşit olmalıdır.","Logaritmanın içi sıfırdan büyük eşit olduğunda, logaritma değeri birden büyük eşit olur.","Çözümde tablo çizerek x değerlerini belirleyip, logaritma ifadelerini eşitleyerek doğru cevaba ulaşılır."]},"beginTime":1283,"endTime":1449,"href":"/video/preview/2933767120302784548?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=1283&ask_summarization=1"},{"index":12,"title":"Logaritma Kuralı Kullanımı","list":{"type":"unordered","items":["Farklı tabanlı logaritma ifadelerini birleştirmek için tabanları eşitlemek gerekir.","Aynı tabanlı logaritma ifadelerinin toplamı, logaritmanın içlerinin çarpımına eşittir.","Logaritma a tabanında b eşittir bir bölü logaritma b tabanında a kuralı kullanılarak soru çözülebilir."]},"beginTime":1449,"endTime":1704,"href":"/video/preview/2933767120302784548?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=1449&ask_summarization=1"},{"index":13,"title":"Video Kapanışı","list":{"type":"unordered","items":["Videoda çözülen sorular genellikle zor değildir, ancak bazı detayları görmek ve tutmak gerekir.","Konuşmacı, daha fazla soru çözmek için başka bir video yapabileceğini belirtiyor.","Konuşmacı, kitabın başlangıç, giriş ve orta seviye için uygun olduğunu ve hızlı bitirilebileceğini söylüyor."]},"beginTime":1704,"endTime":1756,"href":"/video/preview/2933767120302784548?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=1704&ask_summarization=1"}],"linkTemplate":"/video/preview/2933767120302784548?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Logarithm Basic/Easy Question Solution (Logarithm from 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on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/alge... Intro to logarithms. Learning that logarithms are just a...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/4411994/4aae14e6320a0a29d53659450818def4/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/hr/NbSHAAAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"1","reqid":"1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DZ5myJ8dg_rM","linkTemplate":"/video/preview/17411028171623792775?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Logarithms | Logarithms | Algebra II | Khan 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#aytmath #aytcamp logarithm, logarithm explanation, logarithm 12th grade, logarithm properties, Mustached Math. Welcome to AYT Math Camp. CAMP Program PDF: ✔ My Homework PDF...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/902245/3b5d85b62757b05c0a4bf27e6a226a3e/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/lqEaQgIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"2","reqid":"1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=videoid:13101226536184301016","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeninin 80 Günde Matematik Kampı serisinin 41. gününde sunduğu eğitim içeriğidir. Öğretmen, logaritma konusunun beşinci dersini anlatmaktadır.","Video, logaritmanın temel özelliklerini detaylı şekilde ele almaktadır. Öğretmen önce logaritmanın temel kurallarını açıklamakta, ardından logaritma ifadelerinde baştaki sayının veya tabanın üstündeki kuvvetin nasıl başa alınabileceğini örneklerle göstermektedir. Video boyunca 41'den 48'e kadar olan logaritma problemleri adım adım çözülmekte ve farklı çözüm yöntemleri sunulmaktadır.","Öğretmen, konuyu pekiştirmek için çeşitli örnekler çözmekte ve öğrencilerin ödev olarak altın kitabın ikinci ve üçüncü testlerini çözmelerini istemektedir. Video, 6. derste logaritmanın en önemli özelliklerinden birinin işleneceği bilgisiyle sonlanmaktadır."]},"endTime":2222,"title":"80 Günde Matematik Kampı: Logaritma Özellikleri","beginTime":0}],"fullResult":[{"index":0,"title":"Logaritma Kampı ve Özelliklerine Giriş","list":{"type":"unordered","items":["Matematik kampının 41. gününde logaritmanın beşinci dersine başlanıyor ve logaritmanın özellikleri ele alınacak.","Logaritma kampı sonunda, oynatma listesi oluşturulacak ve altın kitabın içerisindeki ekstra yorum isteyen sorular çözülecek.","Öğrencilerden logaritma bitti diyene kadar soru çözmeleri ve logaritmanın beş-altı derslerini dinledikten sonra altın kitabın ikinci ve üçüncü testlerini çözmeleri bekleniyor."]},"beginTime":0,"endTime":105,"href":"/video/preview/13101226536184301016?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=0&ask_summarization=1"},{"index":1,"title":"Logaritmanın Temel Özellikleri","list":{"type":"unordered","items":["Logaritmanın tabanındaki sayı ile yanındaki sayı aynıysa (log_a(a)), logaritmanın sonucu 1'dir.","Logaritmanın yanındaki sayı 1 ise (log_a(1)), logaritmanın sonucu 0'dır.","Bu özellikler, logaritma sorularında hızlıca cevap bulmak için kullanılabilir."]},"beginTime":105,"endTime":270,"href":"/video/preview/13101226536184301016?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=105&ask_summarization=1"},{"index":2,"title":"Logaritma Özelliklerinin Uygulanması","list":{"type":"unordered","items":["Örnek sorularda logaritma özellikleri kullanılarak basit hesaplamalar yapılıyor.","Logaritma özellikleri, karmaşık soruları daha basit hale getirerek çözme imkanı sağlıyor.","Logaritma özellikleri ispat serisinde kara tahtada gösterilecek ve ilgilenenler için ispat videoları oynatma listesi oluşturulacak."]},"beginTime":270,"endTime":487,"href":"/video/preview/13101226536184301016?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=270&ask_summarization=1"},{"index":3,"title":"Logaritmanın Üst Özellikleri","list":{"type":"unordered","items":["Logaritmanın üst özelliği: Eğer logaritmanın yanındaki sayının üstünde bir kuvvet varsa, bu kuvvet logaritmanın başına çarpı olarak alınabilir.","Örneğin, log_a(y^n) = n * log_a(y) formülü kullanılarak hesaplamalar yapılıyor.","Bu özellik, logaritma sorularında üstlere sahip sayıları kolayca işlemek için kullanılıyor."]},"beginTime":487,"endTime":604,"href":"/video/preview/13101226536184301016?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=487&ask_summarization=1"},{"index":4,"title":"Logaritma Özellikleri","list":{"type":"unordered","items":["Bir sayı çarpı logaritma ifadesinde, sayı logaritmanın yanındaki sayının üstüne alınabilir.","Örneğin, 3 × log₇5 ifadesi log₇5³ şeklinde yazılabilir.","Tabanın üstünde kuvvet varsa, bu kuvvet başa alınabilir ancak takla atarak (örneğin 1/b yerine b şeklinde)."]},"beginTime":607,"endTime":702,"href":"/video/preview/13101226536184301016?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=607&ask_summarization=1"},{"index":5,"title":"Tabanın Üstünü Başa Alma","list":{"type":"unordered","items":["Log₂³₂ ifadesinde, tabanın üstündeki 1/3 başa alınarak log₂₂ = 1 olduğundan cevap 1/3 olur.","Log₃²⁵₃ ifadesinde, tabanın üstündeki 5/2 başa alınarak log₃₃ = 1 olduğundan cevap 5/2 olur.","Karekök ifadeleri de tabanın üstü olarak yazılabilir, örneğin √2 = 2^(1/2)."]},"beginTime":702,"endTime":815,"href":"/video/preview/13101226536184301016?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=702&ask_summarization=1"},{"index":6,"title":"Özelliklerin Birleştirilmesi","list":{"type":"unordered","items":["logₓᵇ(yᵃ) ifadesinde, a başa normal olarak, b ise 1/b şeklinde başa alınır.","Taban ve yanındaki sayı aynı tabana indirgenerek işlem yapılır.","Örneklerde, log₄₃₂, log₂₇₃⁻¹, log₂√₂₈ gibi ifadeler çözülerek cevaplar bulunur."]},"beginTime":815,"endTime":1022,"href":"/video/preview/13101226536184301016?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=815&ask_summarization=1"},{"index":7,"title":"Özel Durumlar","list":{"type":"unordered","items":["Taban gizli olduğunda (log₁₀), 10 tabanında işlem yapılır.","log₁₀(1/100) = log₁₀(10⁻²) = -2 olarak çözülür.","e tabanında logaritma durumunda, logₑ(e⁵/³) = 5/3 olarak hesaplanır."]},"beginTime":1022,"endTime":1078,"href":"/video/preview/13101226536184301016?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=1022&ask_summarization=1"},{"index":8,"title":"Logaritma Problemleri Çözümü","list":{"type":"unordered","items":["Videoda logaritma problemleri çözülüyor ve çözüm mantığı anlatılıyor.","İlk soruda logaritma tabanları e olan ifade çözülüyor ve cevap C şıkkı olarak bulunuyor.","İkinci soruda farklı tabanlarda logaritma işlemleri yapılıyor ve cevap E şıkkı olarak hesaplanıyor."]},"beginTime":1078,"endTime":1239,"href":"/video/preview/13101226536184301016?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=1078&ask_summarization=1"},{"index":9,"title":"Karmaşık Logaritma Problemleri","list":{"type":"unordered","items":["Daha karmaşık bir logaritma problemi çözülüyor, iç içe logaritma işlemleri yapılıyor.","Üçüncü soruda tabanları eşitleyerek ve logaritma özellikleri kullanarak cevap A şıkkı olarak bulunuyor.","Dördüncü soruda tabanları eşitleyerek ve logaritma özellikleri kullanarak cevap A şıkkı olarak hesaplanıyor."]},"beginTime":1239,"endTime":1454,"href":"/video/preview/13101226536184301016?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=1239&ask_summarization=1"},{"index":10,"title":"Zor Logaritma Problemleri","list":{"type":"unordered","items":["Beşinci soruda doğal logaritma (taban e) ve farklı tabanlarda logaritma işlemleri yapılıyor.","Altıncı soruda logaritma a tabanında b = x şeklinde verilen bir problem çözülüyor.","Son soruda iki farklı yöntemle çözüm gösteriliyor: logaritma özellikleri kullanarak ve logaritmadan kurtularak."]},"beginTime":1454,"endTime":1721,"href":"/video/preview/13101226536184301016?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=1454&ask_summarization=1"},{"index":11,"title":"Logaritma Soruları Çözümü","list":{"type":"unordered","items":["Logaritma sorularında üstün üstü özelliğini kullanarak ifadeleri basitleştirmek mümkündür.","Üstün 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Eğitmen, tahtada veya dijital platformda matematiksel işlemler yaparak soruları çözmektedir.","Videoda logaritma tanım testi soruları adım adım çözülmektedir. İlk bölümde logaritma tabanında faktöriyel, iç içe kökler, mutlak değer ve logaritma denklemleri ele alınırken, ikinci bölümde 8. sorudan 14. soruya kadar olan logaritma ve üstel denklemler soruları çözülmektedir. Video, logaritmanın tanım kümesine geçiş yaparak sona ermektedir.","Eğitmen, her soru için detaylı çözüm yöntemlerini göstermekte, logaritma özellikleri, üstel denklemlerin çözümü ve logaritma-üstel fonksiyonların tersi gibi konuları ele almaktadır. Bazı soruların çözümünde dönüşüm yöntemleri (örneğin, 2 üzeri x yerine u dönüşümü) kullanılmaktadır."]},"endTime":1156,"title":"Logaritma ve Üstel Denklemler Çözüm Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Logaritma Tanım Testi","list":{"type":"unordered","items":["Logaritma tabanında k faktöriyel ifadesi, k'nın faktöriyeli 1'e eşitse k'nın 1 veya 0 şeklinde iki farklı değeri olabilir.","Logaritma ifadelerinde içeriden dışarı doğru veya dışarıdakileri aşağıya yollayarak üstü ifade olarak yazarak çözüm yapılabilir.","Logaritma ifadelerinde taban ve logaritma değeri arasındaki ilişkiyi kullanarak x'in değeri bulunabilir."]},"beginTime":9,"endTime":104,"href":"/video/preview/3842612028958908054?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=9&ask_summarization=1"},{"index":1,"title":"Logaritma Özellikleri ve Çözümleri","list":{"type":"unordered","items":["Logaritma ifadelerinde taban ve logaritma değeri arasındaki 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gösteriyor."]},"beginTime":618,"endTime":723,"href":"/video/preview/3842612028958908054?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=618&ask_summarization=1"},{"index":6,"title":"Logaritma Özellikleri ve Denklemler","list":{"type":"unordered","items":["x^(ln x) = e⁹ denklemi için x = e^u dönüşümü yapılıyor ve logₑ(e^u) = u olarak hesaplanıyor.","logₑ(e^u) = 9 denkleminden u = 3 veya u = -3 bulunuyor, bu da x = e³ veya x = e⁻³ olarak sonuçlanıyor.","10²ˣ⁺¹ = 4×5ˣ denklemi için 10²ˣ = 100⁰ˣ ve 5ˣ = 20⁰ˣ dönüşümleri yapılıyor, sonuç olarak x = log₂₀(2) bulunuyor."]},"beginTime":723,"endTime":966,"href":"/video/preview/3842612028958908054?parent-reqid=1769421969443236-12038674069899646072-balancer-l7leveler-kubr-yp-vla-242-BAL&text=Logarithm&t=723&ask_summarization=1"},{"index":7,"title":"Fonksiyon Tersleri","list":{"type":"unordered","items":["f(x) = 3ˣ + 1 fonksiyonunun tersi f⁻¹(x) = log₃(x) - 3 olarak hesaplanıyor.","f(x) = 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