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#aytmath #aytcamp Welcome to the Mustache Math AYT Math Camp. Our AYT Math Camp topics will be completed in a planned manner in 74 days. Once our AYT Math topic explanations are...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/4067376/5d3a2649fffdd5a0967995c7f0769239/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/0AJyGwIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"7","reqid":"1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=videoid:14443032375284015090","teaser":[{"list":{"type":"unordered","items":["Bu video, Selim Hoca olarak tanıtılan bir matematik öğretmeninin logaritmalı denklemler konusunu anlattığı kapsamlı bir eğitim içeriğidir. Öğretmen, öğrencilere hitap ederek konuyu adım adım açıklamaktadır.","Videoda 84. sorudan 102. soruya kadar olan logaritmalı denklemler problemleri çözülmektedir. Öğretmen, logaritmanın tanım kümesi, logaritma özellikleri, taban değiştirme, denklemlerin çarpanlarına ayrılması ve ikinci dereceden denklem çözme gibi konuları ele almaktadır. Her soru için detaylı çözüm adımları gösterilmekte ve öğrencilerin dikkat etmesi gereken noktalar vurgulanmaktadır.","Video sonunda öğretmen, logaritmalı eşitsizlikler, logaritma fonksiyonunun grafiği ve logaritma uygulamaları konularının bir sonraki videoda işleneceğini belirtmektedir. Ayrıca öğrencilere \"Altı Test Logaritma\" videosunu izlemelerini ve test altı'yı çözmelerini tavsiye etmektedir."]},"endTime":2954,"title":"Logaritmalı Denklemler Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Logaritmalı Denklemlere Giriş","list":{"type":"unordered","items":["Öğretmen, logaritmanın özelliklerini bitirdikten sonra logaritmalı denklemlere geçiş yapıyor.","Logaritmalı denklemleri çözmek için önceki özelliklerle denklemleri düzenlemek önemlidir.","Videoda 158. sayfadan 162. sayfaya kadar olan 84. sorudan 102. soruya kadar olan sorular çözülecek."]},"beginTime":0,"endTime":46,"href":"/video/preview/14443032375284015090?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=0&ask_summarization=1"},{"index":1,"title":"Ödev Bilgisi","list":{"type":"unordered","items":["Videodan sonra logaritmalı denklem konusunu izleyip, Test 6'ı çözecekler.","Öğretmen kahve içiyor ve sıcaklığından şikayet ediyor."]},"beginTime":46,"endTime":101,"href":"/video/preview/14443032375284015090?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=46&ask_summarization=1"},{"index":2,"title":"Logaritmalı Denklemlerin Çözüm Yöntemleri","list":{"type":"unordered","items":["Logaritma a tabanında fx = b şeklinde bir denklemde, fx = a üzeri b şeklinde yazıp çözmeli ve fx'in sıfırdan büyük olması gerektiğini unutmamalıyız.","İki logaritmanın eşit olması durumunda (log_a(fx) = log_a(gx)), fx = gx olmalı ve her iki fonksiyon da sıfırdan büyük olmalıdır.","Tabanında x olan logaritmalar için, tabanın sıfırdan büyük ve 1'e eşit olmaması, ayrıca fonksiyonların da sıfırdan büyük olması gerekir."]},"beginTime":101,"endTime":274,"href":"/video/preview/14443032375284015090?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=101&ask_summarization=1"},{"index":3,"title":"Örnek Soru Çözümü","list":{"type":"unordered","items":["84. soruda log_3(x+2) = 7 denklemi verilmiş.","Üçün hiçbir tam sayı kuvveti yedi olmadığı bilinmektedir, ancak reel sayılarda bir çözüm vardır.","Çözüm için x+2 = 3^7 şeklinde yazılmalı ve 2 değeri karşıya atılmalıdır."]},"beginTime":274,"endTime":301,"href":"/video/preview/14443032375284015090?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=274&ask_summarization=1"},{"index":4,"title":"Logaritma ve Üslü Sayılar Soruları","list":{"type":"unordered","items":["x = log₃(7) - log₃(2) denklemi çözülerek x = log₃(7/2) olarak bulunmuş ve cevabın Bursa olduğu belirtilmiş.","2^x = 5^(x+1) denklemi, her iki tarafın 5^x ile bölünmesiyle 2/5^x = 5 şeklinde yazılarak x = log₂/₅(5) olarak çözülmüş ve cevabın Adana olduğu belirtilmiş.","x = log₃(7) ve y = log₇(4) olan x.y çarpımı log₃(4) olarak bulunmuş ve cevabın Adana olduğu belirtilmiş."]},"beginTime":305,"endTime":485,"href":"/video/preview/14443032375284015090?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=305&ask_summarization=1"},{"index":5,"title":"Üslü Denklemler ve Logaritma","list":{"type":"unordered","items":["3^x+2 - 3^x+1 = 12 denklemi, ortak çarpan parantezine alınarak 3^x+1(3-1) = 12 şeklinde yazılarak x = log₃(2) veya x = log₃(6) - 1 olarak çözülmüş.","4^x - 5.2^x - 6 = 0 denklemi, 2^x = a dönüşümüyle çözerken a = 6 bulunmuş ve x = log₂(6) olarak hesaplanmış, cevabın Denizli olduğu belirtilmiş.","e^x² - 8e^x + 5 = 0 denklemi, e^x = a dönüşümüyle çözüldüğünde kökler toplamı ln(5) olarak bulunmuş ve cevabın Edirne olduğu belirtilmiş."]},"beginTime":485,"endTime":891,"href":"/video/preview/14443032375284015090?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=485&ask_summarization=1"},{"index":6,"title":"Logaritma Özellikleri","list":{"type":"unordered","items":["3^x = 2 denklemi verilmiş ve log₉(12) değerinin x ve y cinsinden ifadesi sorulmuş."]},"beginTime":891,"endTime":923,"href":"/video/preview/14443032375284015090?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=891&ask_summarization=1"},{"index":7,"title":"Logaritma Özellikleri ve Denklemler","list":{"type":"unordered","items":["Logaritma özellikleri kullanılarak x = log₃(2^y) denklemi çözülüyor ve x/y oranı log₃(2) olarak bulunuyor.","Verilen logaritma ifadeleri üç tabanına dönüştürülerek ve logaritma özellikleri kullanılarak sorunun çözümü tamamlanıyor.","Logaritma denklemlerinde logaritmanın tanımlı olması için x+3>0 şartının sağlanması gerektiği vurgulanıyor."]},"beginTime":926,"endTime":1282,"href":"/video/preview/14443032375284015090?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=926&ask_summarization=1"},{"index":8,"title":"Standart Logaritmalı Denklemler","list":{"type":"unordered","items":["Logaritma özellikleri kullanılarak denklemler çözülüyor ve çarpanlara ayırma yöntemiyle x değerleri bulunuyor.","Logaritmanın tanımlı olması için gerekli şartlar kontrol ediliyor ve çözüm kümesi belirleniyor.","Üslü ve köklü sayılarla ilgili işlemler yaparak denklemler çözülüyor ve x'in değerleri bulunuyor."]},"beginTime":1282,"endTime":1584,"href":"/video/preview/14443032375284015090?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=1282&ask_summarization=1"},{"index":9,"title":"Logaritma Soruları Çözümü","list":{"type":"unordered","items":["Öğretmen, sekiz tane logaritma sorusu çözeceğini belirtiyor.","İlk soruda (95. soru), logaritma ifadeleri kullanılarak x'in 21/2 olarak bulunması gösteriliyor.","İkinci soruda (96. soru), farklı tabanlı logaritma ifadeleri eşitlenerek x'in 2 üzeri 12 olarak hesaplanması gösteriliyor."]},"beginTime":1587,"endTime":1905,"href":"/video/preview/14443032375284015090?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=1587&ask_summarization=1"},{"index":10,"title":"Üçüncü Logaritma Sorusu","list":{"type":"unordered","items":["Üçüncü soruda (97. soru), logaritma ifadelerinde tabanlar eşit değilse, ikisinin de 3'ün kuvveti olduğu kullanılarak çözüm yapılıyor.","x'in karekökü, x+2 ifadesine eşitlenerek x'in 2 veya -1 olarak bulunması gösteriliyor.","Logaritmanın tanımlı olması için x'in 0'dan büyük olması gerektiği belirtilerek, sorunun cevabının 2 olduğu sonucuna varılıyor."]},"beginTime":1905,"endTime":2035,"href":"/video/preview/14443032375284015090?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=1905&ask_summarization=1"},{"index":11,"title":"Logaritma Özellikleri ve Çözümlü Sorular","list":{"type":"unordered","items":["Logaritma x kare ve logaritma x'in karesi ifadeleri farklıdır; logaritma x'in karesi komple logaritma x'in karesini alır ve üzerinde işlem yapılamaz.","98. soruda logaritma 3 tabanında x'in karesi ifadesi kullanılarak denklem çözülür ve x=1/3 olarak bulunur.","99. soruda logaritma 5 tabanında x ve x tabanında 25 ifadeleri kullanılarak denklem çözülür ve x=25 veya x=1/5 olarak bulunur."]},"beginTime":2040,"endTime":2361,"href":"/video/preview/14443032375284015090?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=2040&ask_summarization=1"},{"index":12,"title":"Logaritma Denklemleri ve Şartlar","list":{"type":"unordered","items":["100. soruda logaritma 3 tabanında x kare eksi 13 ifadesi kullanılarak denklem çözülür ve x=4 veya x=-4 olarak bulunur, ancak x≠4 şartı nedeniyle sadece x=-4 kabul edilir.","101. soruda yer değiştirme özelliği kullanılarak denklem çözülür ve x=e² olarak bulunur.","102. soruda x üzeri ln x kalıbı kullanılarak soru çözülebilir."]},"beginTime":2361,"endTime":2632,"href":"/video/preview/14443032375284015090?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=2361&ask_summarization=1"},{"index":13,"title":"Logaritmik Denklemlerde Yer Değiştirme Yöntemi","list":{"type":"unordered","items":["Yer değiştirme özelliği kullanılarak denklemin her iki tarafı yer değiştirildiğinde aynı ifade elde edilirse, denklemin çözümü için logaritma alınmalıdır.","Verilen denklemde x üzeri x = e üzeri (6+x) şeklinde olduğunda, her iki tarafta logaritma e tabanı alınarak denklem çözülebilir.","Logaritma özellikleri kullanılarak denklem düzenlenir ve ikinci dereceden bir denklem elde edilir, bu denklem çözülerek x'in değerleri bulunur."]},"beginTime":2636,"endTime":2829,"href":"/video/preview/14443032375284015090?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=2636&ask_summarization=1"},{"index":14,"title":"Benzer Soru Örneği","list":{"type":"unordered","items":["Benzer bir soru örneği olarak x üzeri logaritma 2 tabanında x = e üzeri (6+logaritma 2 tabanında x) şeklinde bir denklem verilmiştir.","Bu durumda her iki tarafta logaritma 2 tabanı alınarak denklem çözülebilir.","Logaritmik denklemler konusu tamamlanmış ve logaritmalı eşitsizliklere geçilmesi belirtilmiştir."]},"beginTime":2829,"endTime":2918,"href":"/video/preview/14443032375284015090?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=2829&ask_summarization=1"},{"index":15,"title":"Dersin Sonu ve Gelecek Konular","list":{"type":"unordered","items":["Logaritmik denklemler konusu tamamlanmış ve logaritmalı eşitsizliklere geçileceği belirtilmiştir.","Logaritma fonksiyonun grafiği ve logaritma uygulamaları konularının da işleneceği söylenmiştir.","Öğrencilere trigonometri konusunda zorlanmaları durumunda geriden gelmeleri ve videoları izlemeleri tavsiye edilmiştir."]},"beginTime":2918,"endTime":2954,"href":"/video/preview/14443032375284015090?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=2918&ask_summarization=1"}],"linkTemplate":"/video/preview/14443032375284015090?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Logarithm 8 (Equations with Logarithms) AYT Mathematics Camp | Day 37 | AYT Mathematics Subject D...","related_orig_text":"Logarythm - 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#aytmath #aytcamp Welcome to the Mustache Math AYT Math Camp. Our AYT Math Camp topics will be completed in a planned manner in 74 days. Once our AYT Math topic explanations are...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/1473655/b24ed9abca635a116a2d2fcd1099c119/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/EI-OGwIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"8","reqid":"1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=videoid:13435917294483798186","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeninin logaritma konusunun son kısmını anlattığı eğitim içeriğidir. Öğretmen, \"eldiven giyme töreni\" olarak adlandırdığı bir ders formatında öğrencilere hitap etmektedir.","Videoda logaritmalı eşitsizliklerin çözüm yöntemleri detaylı olarak anlatılmaktadır. Öğretmen önce logaritmanın tanımlı olması için gerekli şartları açıklar, ardından tabanın 1'den büyük (bileşik kesir) veya 0 ile 1 arasında (basit kesir) olması durumunda eşitsizlik çözümünde dikkat edilmesi gereken noktaları örneklerle gösterir. Video, teorik bilgilerin ardından 105. sorudan 109. soruya kadar olan problemlerin çözümüyle devam eder ve \"Altın Test 6\" olarak adlandırılan bir testle sonlanır.","Öğretmen, öğrencilere sınava hazırlanmaları için test çözmelerini ve farklı soruların çözümlerini video çözüm uygulamasından izlemelerini tavsiye eder. Video sonunda logaritma fonksiyonunun grafiği konusuna geçileceği belirtilmektedir."]},"endTime":1252,"title":"Logaritmalı Eşitsizlikler Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Logaritmalı Eşitsizlikler Giriş","list":{"type":"unordered","items":["Logaritmalı eşitsizlikler, logaritmalı denklemlerden farklı olarak araya küçük-büyük işareti girer ve tabana dikkat edilir.","Logaritmalı eşitsizliklerde tabanın bileşik kesir veya basit kesir olma durumuna göre hareket edilir.","Logaritma konusu sona ererken, logaritma eşitsizlikler, logaritma grafikleri ve logaritma uygulamaları konuları ele alınacaktır."]},"beginTime":0,"endTime":99,"href":"/video/preview/13435917294483798186?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=0&ask_summarization=1"},{"index":1,"title":"Logaritmalı Eşitsizliklerin Çözüm Şartları","list":{"type":"unordered","items":["Logaritmalı eşitsizliklerde öncelikle logaritmanın tanımlı olması gerekir: a ≠ 1 ve a > 0, ayrıca logaritmanın içerisindeki f(x) ve g(x) değerlerinin sıfırdan büyük olması şarttır.","Eşitsizliği çözdüğümüzde bu şartları sağlamayan değerler çözüm kümesinden atılır.","Üslü sayılarda, taban 1'den büyük (bileşik kesir) olduğunda kuvvetler büyüdükçe sayı büyür, taban 0'dan 1'e kadar (basit kesir) olduğunda kuvvetler büyüdükçe sayı küçülür."]},"beginTime":99,"endTime":240,"href":"/video/preview/13435917294483798186?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=99&ask_summarization=1"},{"index":2,"title":"Logaritmalı Eşitsizliklerin Çözüm Yöntemi","list":{"type":"unordered","items":["Eğer taban a sayısı 1'den büyük (bileşik kesir) ise, logaritmaları iptal edip aradaki işaretin aynısını koyarız: f(x) ≤ g(x).","Eğer taban a sayısı 0'dan 1'e kadar (basit kesir) ise, aradaki işaretin tam tersini koyarız: f(x) > g(x).","Örnek olarak, log₂(2x-3) > log₂(x) eşitsizliğinde taban 2 bileşik kesir olduğu için 2x-3 > x olur."]},"beginTime":240,"endTime":368,"href":"/video/preview/13435917294483798186?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=240&ask_summarization=1"},{"index":3,"title":"Logaritmik Eşitsizlik Çözümü","list":{"type":"unordered","items":["Logaritmik eşitsizliklerde önce tanım kümesi belirlenir: 3x-7>0 ve x+1>0 şartları çözülür.","Bileşik kesir olduğu için logaritma yok edilir ve 3x-7\u003cx+1 eşitsizliği çözülür, sonuç x\u003c4 bulunur.","Tanım kümesi ile x\u003c4 aralığı birleştirilerek çözüm kümesi 7/3\u003cx\u003c4 olarak belirlenir."]},"beginTime":370,"endTime":445,"href":"/video/preview/13435917294483798186?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=370&ask_summarization=1"},{"index":4,"title":"Farklı Tabanlı Logaritmik Eşitsizlik","list":{"type":"unordered","items":["Farklı tabanlı logaritmik eşitsizliklerde tabanlar aynı duruma getirilir: log₂₇(2x-1) \u003c log₃(2).","Tabanlar aynı hale getirildikten sonra 2x-1\u003c2³ eşitsizliği çözülür ve x\u003c9/2 bulunur.","Tanım kümesi için 2x-1>0 şartı da çözülür ve x>1/2 bulunur, sonuç 1/2\u003cx\u003c9/2 aralığıdır."]},"beginTime":445,"endTime":606,"href":"/video/preview/13435917294483798186?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=445&ask_summarization=1"},{"index":5,"title":"Basit Kesir Tabanlı Eşitsizlik","list":{"type":"unordered","items":["Taban 1/2 olan eşitsizlikte tabanın basit kesir olduğu için eşitsizlik yönü tersine çevrilir.","Tanım kümesi için 2x-6=0 ve x+4=0 şartları çözülür, sonuç x>3 ve x>-4 bulunur.","Eşitsizlik çözülür ve x≤10 bulunur, çözüm kümesi 3\u003cx≤10 aralığıdır ve 7 farklı tam sayı değeri vardır."]},"beginTime":606,"endTime":705,"href":"/video/preview/13435917294483798186?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=606&ask_summarization=1"},{"index":6,"title":"Çarpım Durumunda Logaritmik Eşitsizlik","list":{"type":"unordered","items":["Çarpım durumunda logaritmik eşitsizlikte önce tanım kümesi belirlenir: x>0 ve x-3>0 şartları çözülür.","Eşitsizlik çözülür ve x²-3x-15≤0 bulunur, çarpanlarına ayrılarak (x-5)(x+3)≤0 elde edilir.","Çözüm kümesi (-3,5] aralığıdır, ancak tanım kümesi ile birleştirildiğinde (3,5] aralığı bulunur."]},"beginTime":705,"endTime":849,"href":"/video/preview/13435917294483798186?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=705&ask_summarization=1"},{"index":7,"title":"Farklı Değerlerde Eşitsizlik","list":{"type":"unordered","items":["Eşitsizliğin çözüm kümesi kaç farklı değer alır sorusunda önce tanım kümesi belirlenir: x+4>0.","Eşitsizlik çözülür ve -4\u003cx≤5 bulunur, çözüm kümesinde 9 farklı tam sayı değeri vardır.","Basit kesir tabanlı eşitsizliklerde yön değiştirilirken, bileşik kesir tabanlı eşitsizliklerde yön değişmez."]},"beginTime":849,"endTime":1036,"href":"/video/preview/13435917294483798186?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=849&ask_summarization=1"},{"index":8,"title":"Logaritma Eşitsizliği Çözümü","list":{"type":"unordered","items":["Soruda bir trick bulunuyor ve izleyicilerden bu triki yakalamaları isteniyor.","Logaritma eşitsizliğinin çözümünde önce logaritmanın içindeki ifadenin sıfırdan büyük olması şartı inceleniyor.","Logaritmanın içindeki ifadenin pozitif olması için ikinci bir şart da bulunuyor."]},"beginTime":1045,"endTime":1133,"href":"/video/preview/13435917294483798186?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=1045&ask_summarization=1"},{"index":9,"title":"Eşitsizliğin Çözümü","list":{"type":"unordered","items":["Eşitsizliğin çözümünde önce tabanların basit kesir olup olmadığı kontrol ediliyor.","Basit kesir tabanlarda yön değişirken, bileşik kesir tabanlarda yön değişmez.","Eşitsizliğin çözüm kümesi 3 ile 38 arasında bulunuyor."]},"beginTime":1133,"endTime":1203,"href":"/video/preview/13435917294483798186?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=1133&ask_summarization=1"},{"index":10,"title":"Dersin Sonu ve Öneriler","list":{"type":"unordered","items":["Altın test 6 denklem ve eşitsizlikleri çözülecek, ardından logaritma fonksiyonun grafiği anlatılacak.","Logaritma fonksiyonun grafiği için ayrıntılı bir video paylaşılacak.","Farklı soruların çözümlerinde video çözüm uygulamasından bakılması öneriliyor."]},"beginTime":1203,"endTime":1249,"href":"/video/preview/13435917294483798186?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=1203&ask_summarization=1"}],"linkTemplate":"/video/preview/13435917294483798186?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Logarithm 9 (Inequalities with Logarithms) AYT Mathematics Camp | Day 37 | AYT Mathematics Subjec...","related_orig_text":"Logarythm - Topic","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Logarythm - 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wanted to share some solutions to questions from the logarithm section, which is the first topic in Grade 12 and the AYT exam, which has 2-3 questions. The playlist below contains all the...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3444973/37b95073e8e5134dcb6530a1eee3fcc2/564x318_1"},"target":"_self","position":"9","reqid":"1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D_qoCMNW6BXY","linkTemplate":"/video/preview/15119956654524013698?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Logarithm Basic/Easy Question Solution (Logarithm from Scratch)","related_orig_text":"Logarythm - Topic","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Logarythm - Topic\",\"url\":\"http:\\/\\/www.youtube.com\\/watch?v=_qoCMNW6BXY\",\"src\":\"serp\",\"rvb\":\"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_E9oQggQkAYAEKyqLARABGniB_wT7Af4CAPMKBAEDA_4BCwz2-PYAAAD0EfoCBgL_AAr7-AEAAAAA-P8BDf0AAAD8_AT7_P4AAAEK_wUEAAAAHPkC9f0AAAAL-P_9AAEAAPz4Av8C_wAABwIF-P8AAAD2_PIO_wAAAPr4A_IAAAAAC_H69QAAAAAgAC0T89k7OBNACUhOUAIqcxAAGmAbDwAZHw7p0d3_8_X5Ki_VyAXv-uPtAOPzAPgiGvv76-b69wwATNkBGsEAAAAP_9UyAAAbUOja5An54-K12uYV33_0CwH0Fwng1x367DE23uri9EIA6NIB_vsB8B8SCCIgAC3cVU87OBNACUhvUAIqrwYQDBqgBgAAoEEAANjBAACMQgAALMIAACxCAAAowgAAOEIAAMDBAADKwgAAgEEAAHBBAABAQAAA-MEAAOhBAACIQgAAfMIAADDBAAAEwgAAyMEAAHDBAABswgAAhsIAAKjBAAAMQgAAgEEAAHBBAABQwgAAQMAAAOBBAAC4QgAANMIAAIA_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_AACAwQAA2EEAAOBBAABAwQAAqEEAAIA_AABAQQAAJMIAABDBAACKwgAA8MEAAGDCAAC4QQAANEIAAEDCAABcQgAAEEEAACBBAADAwAAAAMEAALhBAAAAAAAAwEEAADjCAAB4wgAABEIAAABCAACgwAAAgMAAAFxCAACYQQAAQMIAAPhBAABsQgAAqMEAADTCAAAAAAAAjsIAAFhCAAAQQQAAAAAAACRCAABQwgAAQEEAADDCAABcwgAAwMAAAChCAACowQAAgMAAAADCAADgQQAAmMIAAJLCIAA4E0AJSHVQASqPAhAAGoACAACIvQAABL4AAGw-AABEvgAAgDsAAMI-AADGPgAAY78AAAW_AADgvAAA2L0AADS-AADgvAAAFD4AAI6-AADYvQAAgDsAAOA8AADIPQAAaz8AAGs_AACuvgAAiD0AAK6-AADYvQAA6L0AAHw-AAAwPQAALL4AAHQ-AACmPgAABL4AALi9AAAPPwAADD4AALi9AACIPQAAhr4AALK-AAC4vQAALL4AAIA7AACAuwAAsr4AADS-AAA0PgAAiD0AAIC7AABQPQAATL4AADy-AAAEvgAAoLwAABQ-AAD6vgAAED0AAH8_AABUvgAAiD0AAAk_AAB8vgAA5j4AANg9AABAPCAAOBNACUh8UAEqjwIQARqAAgAAqL0AAAQ-AADovQAAJb8AAKC8AAAEPgAApj4AAEA8AABQvQAAmD0AAOC8AAAMvgAAgLsAAKi9AABUPgAAcL0AABC9AAADPwAARL4AAO4-AACovQAA4DwAABC9AAAMvgAAQDwAAAS-AAD4vQAAiD0AADS-AAAwvQAAMD0AAAQ-AAAEvgAAEL0AALg9AABsvgAALD4AAFQ-AABMvgAAQLwAADA9AABQvQAA2L0AAHA9AACovQAA2L0AAH-_AACgvAAAQLwAAAw-AACIPQAADD4AAKi9AACCPgAAcD0AAAQ-AABwvQAAiL0AAMg9AAD4PQAA-D0AABQ-AABMPgAAmL0gADgTQAlIfFABMAk4AUoAYABoAA,,\"}","related_url":"http://www.youtube.com/watch?v=_qoCMNW6BXY","parent-reqid":"1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL","related_vfp":1,"relatedVideo":"yes"},"cwidth":1280,"cheight":720,"cratio":1.77777,"dups":["15119956654524013698"],"episode":0,"season":0,"isEmbedOnly":false,"greenHost":"YouTube","hasTranslation":true,"contentTypeId":null,"censored":false},"13101226536184301016":{"videoId":"13101226536184301016","docid":"12-0-0-Z0E2D5AAA6761DF23","description":"#logarithm #aytmath #aytcamp logarithm, logarithm explanation, logarithm 12th grade, logarithm properties, Mustached Math. 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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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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 üstü özelliğini kullanarak logaritma ifadelerinde üstler başa alınabilir.","Üslü sayı veya köklü sayı bilgisini kullanarak logaritma sorularını çözebilirsiniz."]},"beginTime":1722,"endTime":1790,"href":"/video/preview/13101226536184301016?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=1722&ask_summarization=1"},{"index":12,"title":"Üslü Sayılarla İlgili Logaritma Sorusu","list":{"type":"unordered","items":["Üslü sayılarla ilgili logaritma sorularında, bir değişkenin değerini başka bir değişken cinsinden 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done with logarithms! It's a hefty topic so we have to round out the trilogy. We will definitely need to know how to manipulate logarithmic expressions, whether expanding or condensing...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2215615/fcc488be344344df57c8df388141ada3/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/3_cptgAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"16","reqid":"1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DMSTSBW8LPRM","linkTemplate":"/video/preview/11102595398227448843?parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Logarithms Part 3: Properties of Logs, Expanding Logarithmic Expressions","related_orig_text":"Logarythm - Topic","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Logarythm - Topic\",\"url\":\"http:\\/\\/www.youtube.com\\/watch?v=MSTSBW8LPRM\",\"src\":\"serp\",\"rvb\":\"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_E6kDggQkAYAEKyqLARABGniB_QL7-fwEAOoJAwMKAf8ACwz2-PYAAAD-DgABBQX-AAQJBQD4AQAACAoJBPwAAADvAPj_8QABAAoFAAgEAAAAHPoC9f0AAAALAQoACP8BAPb__AwE_wAADQgBBQAAAAD1_gQBAQAAAPv_BPgAAAAABvr6_fv2_gAgAC2I7947OBNACUhOUAIqhAIQABrwAX8U-__p2PgByALnAboIDgGfMSf_OxXBAL0oDwHK0wIB0zTf_8v6w__jB-AB0eQhAADe7P4b6TwALgPf_yr28__vBBoBOdfWADfrJQDT8gb-9_kt_-b-IP8UH-gBD__hAPgGCvwJ-tYB7AO9AhrjMAMC6Sz8BuYJ_9nGDQHyLBgEP8fx-M0T5wYF3OsI3vQzCPsBJAHzB__-4QMGDCHu0v8B7g8CCODYADj54AP_1Oz6DsH6-tvo2gTmDScE3Q_uA-XuGvjH5u787hcK7hL-7vq95wQKFQYDAeYA7g8czxLx3PHqAeb0FvPf8v0P4Rb_-yAALVJtCTs4E0AJSGFQAipzEAAaYC3yADMfL88bESnazNsLKeXLEMQU8QD_6bj_ACn-ExvZ294QGwAivAoIpAAAAEowvkXRAAp70cfYC_raEoid7BD9f-soBrQNLNmd4tL-FRfo6QQWVADh0rcZ-_vCCh8SASAALUhqFTs4E0AJSG9QAiqvBhAMGqAGAAAEQgAAsEEAAIBBAABYwgAAYEIAADRCAADYQQAAOMIAAODAAABwQQAAcMEAAGTCAACAwgAAiMEAADRCAAA8wgAA8EEAAATCAAA4QgAAqMIAACTCAAAgwQAAsMEAAERCAAAIQgAAmMEAAKjBAABYwgAAEEEAAEBAAAAAQQAAAEIAACDCAAAQwQAAwMEAABBBAACAvwAA8kIAAAjCAACoQgAA4EAAAFDBAABkQgAAgMAAAEBBAAC-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_AACYwQAABMIAAETCAAAoQgAAAMEAAHBBAABgQgAAbMIAAGBCAACQQQAAsMEgADgTQAlIdVABKo8CEAAagAIAAI6-AAC4vQAAQLwAAFC9AAAMPgAAIT8AAAw-AABdvwAA6r4AALi9AADYPQAAhr4AABQ-AAAFPwAAUD0AAAS-AADYvQAAoDwAACS-AAApPwAAfz8AAAy-AABUPgAAgr4AALa-AAAUPgAAyD0AAES-AACYPQAAQDwAAPI-AACovQAAJL4AAKg9AABMPgAAuL0AAMg9AACSvgAA4r4AAIC7AAABvwAAUL0AAJi9AABEvgAAXL4AAGw-AACOPgAARL4AANg9AACKvgAApr4AAN6-AACgPAAAnj4AAL6-AADYPQAAfT8AALi9AACCPgAALT8AAHS-AAAMPgAAdD4AAOC8IAA4E0AJSHxQASqPAhABGoACAABQvQAAqD0AAMi9AAA7vwAADL4AALi9AABwPQAAcD0AAPi9AAAMPgAAuD0AAIa-AACgPAAAlr4AAEQ-AADIvQAAyD0AAA8_AACYPQAAoj4AANg9AACoPQAAXD4AAAy-AACAuwAAQLwAAEy-AAC4PQAA-L0AAKA8AAC4PQAAqD0AAEC8AADovQAAuD0AACy-AACoPQAAij4AAFy-AAAkPgAATD4AAIC7AAAMvgAAyD0AAKC8AAD4PQAAf78AAOC8AACovQAAuD0AAAQ-AAC4vQAAoDwAAEQ-AADoPQAAqD0AAEC8AAAQPQAAEL0AADy-AABAPAAAgj4AAKg9AACovSAAOBNACUh8UAEwCTgBSgBgAGgA\"}","related_url":"http://www.youtube.com/watch?v=MSTSBW8LPRM","parent-reqid":"1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL","related_vfp":1,"relatedVideo":"yes"},"cwidth":1920,"cheight":1080,"cratio":1.77777,"dups":["11102595398227448843"],"episode":0,"season":0,"isEmbedOnly":false,"greenHost":"YouTube","hasTranslation":true,"contentTypeId":null,"censored":false,"videoContentId":"3825697341"},"2933767120302784548":{"videoId":"2933767120302784548","docid":"12-6-0-Z10F0AB17C4087FB4","description":"Greetings. We've been in high demand for easy solutions to logarithms. Today, we've solved easy and basic logarithm problems from Endemik Publications' AYT Math Question Bank. If you'd like us...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/4321481/666f6af58670a8b2fc33240a76f1fbd0/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/KWuZPgIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"17","reqid":"1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=videoid:2933767120302784548","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeninin logaritma ve fonksiyonlar konularını anlattığı kapsamlı bir eğitim içeriğidir. Öğretmen, Endemik Yayınları'nın AYT Matematik Soru Bankası kitabından örnekler kullanarak konuyu ele almaktadır.","Videoda logaritma konusunun temel ve orta düzey soru çözümleri, eşitsizlikler, logaritma grafikleri, mutlak değer fonksiyonları ve bunların grafikleri detaylı olarak anlatılmaktadır. Öğretmen, logaritma kurallarını, fonksiyonların birebir ve örten olma durumlarını, tanım ve değer aralıklarını grafiklerle açıklamakta ve çeşitli problem tiplerini adım adım çözmektedir.","Video, logaritma konusunu anlamakta zorlanan öğrenciler için hazırlanmış olup, asal sayılarla ve küçük sayılarla çalışmanın önemi, kök ve küp kök içeren logaritma ifadelerinin sadeleştirilmesi, fonksiyonların terslerinin alınması ve yeni nesil soru tipleri gibi konuları içermektedir. 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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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=1769053679601800-11064778600858262961-balancer-l7leveler-kubr-yp-klg-262-BAL&text=Logarythm+-+Topic&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 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