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Video, Fatih'in annesinin ve babasının Görkem'i affetmeyi reddetmesi ve Fatih'in babasının Ömer ile konuşmak istemesiyle sona erer."]},"endTime":551,"title":"Aile İçindeki Gerilim ve Hamilelik Sırrı","beginTime":0}],"fullResult":[{"index":0,"title":"Görkem'in Savunması","list":{"type":"unordered","items":["Görkem kendisini suçlayanlara karşı savunmasını yaparak \"ben bir şey yapmadım, kimseye zarar vermedim\" diyerek kendini savunuyor.","Görkem'in yanında bir Allah'ın kulu olmadığı belirtiliyor.","Görkem'in perişan ve hamile olduğu, kendisinin atladığı ve elini bile sürmediği söyleniyor."]},"beginTime":1,"endTime":58,"href":"/video/preview/143027761229157632?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=1&ask_summarization=1"},{"index":1,"title":"Aile Arasındaki Tartışma","list":{"type":"unordered","items":["Görkem'in kafasız kardeşi, onun gibi bir herife aşık olduğunu söylüyor.","Boşanma olmazsa şikayetinden vazgeçtiğini söyledikleri halde, kız \"manyak\" diye cevap veriyor.","Görkem'in amcasıyla olan ilişkisi ve amcanın kızına musallat olduğu, tehdit ettiği ve korkuttuğu belirtiliyor."]},"beginTime":58,"endTime":121,"href":"/video/preview/143027761229157632?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=58&ask_summarization=1"},{"index":2,"title":"Fatih'in Kararı","list":{"type":"unordered","items":["Görkem'in kardeşi Fatih'in adını tekrarladığını söylüyor.","Fatih, yeğeninin babasız büyümeyeceğini ve evlilikte mutlu mesut devam edeceğini belirtiyor.","Kabul etmezse çocuğunu cezaevinden göreceğini söylüyor."]},"beginTime":121,"endTime":196,"href":"/video/preview/143027761229157632?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=121&ask_summarization=1"},{"index":3,"title":"Görkem ve Fatih Arasındaki Konuşma","list":{"type":"unordered","items":["Fatih, Görkem'i ittiğini söylediğini hatırlatıyor.","Görkem, hamile olduğunu ve Ömer ile aralarında hiçbir şey olmadığını yemin ediyor.","Fatih, Görkem'in amcasıyla olan ilişkisini ve yalanlarını affedemeyeceğini söylüyor."]},"beginTime":196,"endTime":258,"href":"/video/preview/143027761229157632?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=196&ask_summarization=1"},{"index":4,"title":"Görkem'in İtirafı","list":{"type":"unordered","items":["Görkem, Fatih'e hastalandığını ve tedaviye ihtiyacı olduğunu söylüyor.","Fatih, Görkem'in iyileşeceğini ve üzdüğü herkesin gönlünü alacağını söylüyor.","Görkem, Fatih'e çok aşık olduğunu ve sensiz yaşayamayacağını itiraf ediyor."]},"beginTime":258,"endTime":310,"href":"/video/preview/143027761229157632?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=258&ask_summarization=1"},{"index":5,"title":"Hamilelik ve Şikayet","list":{"type":"unordered","items":["Görkem, bebeğinin tutunduğunu ve hamile olduğunu söylüyor.","Fatih, şikayetini geri çektiğini belirtiyor.","Görkem, Fatih'in iftiralarından kurtulmak için bunu yaptığını söylüyor."]},"beginTime":310,"endTime":379,"href":"/video/preview/143027761229157632?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=310&ask_summarization=1"},{"index":6,"title":"Aile İçindeki Gerilim","list":{"type":"unordered","items":["Görkem'in annesi, kızının şikayetini geri çekmesine dua etmelerini istiyor.","Resul Bey, iftira attığını söylüyor.","Abdullah Bey, kızının içeride yatarken nasıl sakin olabileceğini soruyor."]},"beginTime":379,"endTime":429,"href":"/video/preview/143027761229157632?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=379&ask_summarization=1"},{"index":7,"title":"Görkem'in Durumu","list":{"type":"unordered","items":["Görkem'in bir iki gün kalması gerektiği belirtiliyor.","Görkem'in evde güvende olup olmadığı sorgulanıyor.","Görkem'in kendi ısrarıyla kaldığı söyleniyor."]},"beginTime":429,"endTime":476,"href":"/video/preview/143027761229157632?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=429&ask_summarization=1"},{"index":8,"title":"Amcanın Kaçışı","list":{"type":"unordered","items":["Amcanın kaçtığı ve nerede olduğu bilinmiyor.","Amcanın karıya musallat olduğu belirtiliyor.","Abdullah Bey, amcanın evine gideceğini söylüyor."]},"beginTime":476,"endTime":523,"href":"/video/preview/143027761229157632?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=476&ask_summarization=1"}],"linkTemplate":"/video/preview/143027761229157632?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Görkem asks Fatih for another chance! 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Dönem 1. Yazili SORU... 12.Sinif Matematik DERS Kitabi Sayfa 67 68 69 70 71 72 ✏️ 12.Sinif...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/1999465/a4bb2871fb89471d8ae5ad6abcd4ea94/564x318_1"},"target":"_self","position":"8","reqid":"1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=videoid:14267483017070210220","teaser":[{"list":{"type":"unordered","items":["Bu video, bir öğretmenin 12. sınıf matematik ders kitabındaki üstel ve logaritmik fonksiyonlar konusundaki soruları çözdüğü eğitim içeriğidir.","Videoda toplam 34 sorudan oluşan bir soru seti adım adım çözülmektedir. Öğretmen, üstel fonksiyonların özellikleri, logaritma fonksiyonları, doğal logaritma, fonksiyonların grafikleri, ters fonksiyonları, logaritma denklemleri, eşitsizlikleri ve fonksiyonların artan-azalan durumları gibi konuları ele almaktadır.","Video, boş bırakılan yerlere uygun ifadeler yazma, doğru-yanlış soruları, eşleştirme, fonksiyonların değerlerini bulma, logaritma değerlerinin yaklaşık hesaplanması, ses düzeyi hesaplamaları ve nüfus artış hızı gibi çeşitli soru tiplerini içermektedir. Her soru için detaylı çözüm adımları verilmekte ve grafikler üzerinden açıklamalar yapılmaktadır."]},"endTime":3659,"title":"12. Sınıf Matematik: Üstel ve Logaritmik Fonksiyonlar Soru Çözümleri","beginTime":0}],"fullResult":[{"index":0,"title":"Üstel ve Logaritmalı Fonksiyonlar Ünitesi","list":{"type":"unordered","items":["12. sınıf matematik ders kitabının sayfa 67'deki ünite değerlendirme soruları çözülecek.","Bu ünitede üst üstel ve logaritmalı fonksiyonlar işlenmiş."]},"beginTime":1,"endTime":14,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=1&ask_summarization=1"},{"index":1,"title":"Boş Bırakılan Yerlere Uygun İfadeler","list":{"type":"unordered","items":["Üstel fonksiyonun tabanı a, a>0 ve a≠1 olmalıdır.","Üst üstel fonksiyon birebirdir çünkü farklı değerler farklı görüntülere gider.","Üst üstel fonksiyonun ters fonksiyonu logaritma fonksiyonudur.","Tabanı e olan logaritma fonksiyonuna doğal logaritma fonksiyonu denir.","Logaritma fonksiyonlarının grafikleri x eksenini keserken y eksenini kesemez."]},"beginTime":14,"endTime":123,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=14&ask_summarization=1"},{"index":2,"title":"Doğru-Yanlış Soruları","list":{"type":"unordered","items":["0,1 aralığında logaritma fonksiyonu azalandır, artandır ifadesi yanlıştır.","Logaritma fonksiyonları birebirdir ifadesi doğrudur.","Logaritma kuralı yanlış yazılmıştır, doğru olan ifade logₐ(x·y) = logₐ(x) + logₐ(y) şeklindedir.","Üstel fonksiyonun grafiği ile logaritma fonksiyonunun grafiği y=x doğrusuna göre simetriktir ifadesi doğrudur.","1 üzeri x fonksiyonu üstel fonksiyondur ifadesi yanlıştır, çünkü üstel fonksiyonun tabanı 1 olamaz."]},"beginTime":123,"endTime":234,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=123&ask_summarization=1"},{"index":3,"title":"Eşleştirme Sorusu","list":{"type":"unordered","items":["ln(e) = 1, log₁₀(x) = 2 için x = 0,1², log₁₀(x) = 10,5 için x = 100, log₁₀(x) = e için x = 10ⁿ, ln(e) = 10 için x = e¹⁰."]},"beginTime":234,"endTime":338,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=234&ask_summarization=1"},{"index":4,"title":"Üstel Fonksiyon Problemleri","list":{"type":"unordered","items":["f(x) = (3/2)ˣ fonksiyonu için x = -3 için f(x) = 27/8, x = 1 için f(x) = 3/2, x = -1/2 için f(x) = 1/2, x = 2 için f(x) = 4/9.","Grafikteki a, b, c değerleri için a = 8/27, b = 1, c = -2 olarak bulunmuştur."]},"beginTime":338,"endTime":567,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=338&ask_summarization=1"},{"index":5,"title":"Üstel Fonksiyon Tanımı ve Azalan Fonksiyon","list":{"type":"unordered","items":["Üstel fonksiyon f(x) = aˣ şeklinde tanımlanır, burada a>0 ve a≠1 olmalıdır.","f(x) = (3k-1)ˣ fonksiyonu azalan olduğuna göre k'nın değer aralığı 1/3 \u003c k \u003c 2/3'tür."]},"beginTime":567,"endTime":675,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=567&ask_summarization=1"},{"index":6,"title":"Logaritma ve Fonksiyon Soruları","list":{"type":"unordered","items":["Yedinci soruda, sayıların kuvvetleri hesaplanarak ve tabanlar eşit olduğunda üstlerin oranının alınmasıyla sonuç 53/6 olarak bulunuyor.","Sekizinci soruda, fonksiyonun tanımlı olabilmesi için köklü ifadelerde kök içi ≥0 ve logaritmalı ifadelerde her zaman pozitif olması gerekiyor.","Dokuzuncu soruda, logaritma fonksiyonunun görüntü kümesi en fazla 0, en az -∞ olabilir çünkü 1/1+x² ifadesi 0'dan büyük olur ve azalan bir fonksiyon olduğundan logaritma negatif sayılara gider."]},"beginTime":682,"endTime":942,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=682&ask_summarization=1"},{"index":7,"title":"Logaritma Özellikleri ve Fonksiyon Tersleri","list":{"type":"unordered","items":["Onuncu soruda, logaritma fonksiyonunun değerleri kullanılarak k değeri -25 olarak bulunuyor.","On birinci soruda, logaritma ifadelerinin toplamı hesaplanırken tanjant ve kotanjant özellikleri kullanılarak sonuç 0 olarak bulunuyor.","On ikinci soruda, logaritma fonksiyonunun grafiği kullanılarak f(81) + f(1/27) değeri -1 olarak bulunuyor."]},"beginTime":942,"endTime":1193,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=942&ask_summarization=1"},{"index":8,"title":"Logaritma Denklemleri ve Uygulamaları","list":{"type":"unordered","items":["On üçüncü soruda, logaritma özellikleri kullanılarak ifadenin değeri 3 olarak bulunuyor.","On dördüncü soruda, logaritma taban değiştirme kuralı kullanılarak log₆2 ifadesi k cinsinden 1/k + 1 olarak bulunuyor.","On beşinci soruda, fonksiyonun tersi alınarak f⁻¹(x) = ln(x)/3 olarak bulunuyor."]},"beginTime":1193,"endTime":1388,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=1193&ask_summarization=1"},{"index":9,"title":"Dik Üçgen ve Logaritma Denklemleri","list":{"type":"unordered","items":["On altıncı soruda, dik üçgenin alanı hesaplanarak 1 olarak bulunuyor.","On yedinci soruda, logaritma denklemi çözülerek x = ln(2) olarak bulunuyor.","On sekizinci soruda, x \u003c y olmak üzere x+y=11 ve log(x)+log(y)=1 koşulları verilmiş."]},"beginTime":1388,"endTime":1514,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=1388&ask_summarization=1"},{"index":10,"title":"Logaritma Problemleri","list":{"type":"unordered","items":["Logaritma x çarpı y eşittir bir gizli on olduğunda, x çarpı on üzeri bir'den on bulunur.","Çarpımları on, toplamları onbir olan iki tam sayı x=10 ve y=1'dir, logaritma x/y = -1 olarak hesaplanır.","Eşitsizliği sağlayan x tam sayıları için ln x² - 4x ≤ ln 21 denklemi çözülür ve x değeri -5 ile 5 aralığında bulunur."]},"beginTime":1533,"endTime":1694,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=1533&ask_summarization=1"},{"index":11,"title":"Logaritma Eşitlikleri","list":{"type":"unordered","items":["Logaritma m = logaritma k + logaritma m eşitliğinde, tabanlar eşit olduğundan logaritma k çarpı m = logaritma k artı m olur.","Denklem çözülürse m = k/(k-1) olarak bulunur.","Logaritma 7 yaklaşık olarak 0,85 olduğuna göre, logaritma 7 üzeri 70 sayısı 59,15 ile 60 arasında bulunur."]},"beginTime":1694,"endTime":1855,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=1694&ask_summarization=1"},{"index":12,"title":"Ses Düzeyi Problemi","list":{"type":"unordered","items":["Ses düzeyi L = 10 × log₁₀(I) desibel formülüyle hesaplanır.","Ses düzeyi 90 desibelden 110 desibele çıkarıldığında, ses şiddeti 100 katına çıkmıştır."]},"beginTime":1855,"endTime":1974,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=1855&ask_summarization=1"},{"index":13,"title":"Üstel Fonksiyonlar","list":{"type":"unordered","items":["f(x) = 2ˣ üstel fonksiyonu artan fonksiyondur çünkü taban 1'den büyüktür.","f(x) = 2ˣ fonksiyonu çift fonksiyon değildir çünkü f(-x) = 2⁻ˣ = 1/2ˣ'dir.","f(x) = (1/3)ˣ azalan bir üstel fonksiyondur çünkü taban 1'den küçüktür."]},"beginTime":1974,"endTime":2160,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=1974&ask_summarization=1"},{"index":14,"title":"Fonksiyon Tanım Kümesi ve Grafiği","list":{"type":"unordered","items":["Fonksiyonun en geniş tanım kümesi için tabanın 1'den büyük ve sıfırdan büyük olması gerekir.","f(x) = -log₂(x) fonksiyonunun grafiği, tabanın 0,5 olduğu için azalan bir fonksiyondur."]},"beginTime":2160,"endTime":2286,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=2160&ask_summarization=1"},{"index":15,"title":"Fonksiyon Grafiği Sorusu","list":{"type":"unordered","items":["A şıkkı azalan bir fonksiyon grafiği olabilir, B şıkkı artan yukarı doğru gidiyor, C şıkkı azalan bir fonksiyon olabilir, D ve E şıkları artan.","Logaritmada logaritması alınan bir ifadenin negatif olmaması gerekiyor, bu nedenle fonksiyonun grafiğinin x ekseninin negatif tarafına gitmemesi gerekiyor.","C şıkkında negatif bir değer için görüntüler var, bu nedenle grafik olarak cevap olamaz."]},"beginTime":2290,"endTime":2351,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=2290&ask_summarization=1"},{"index":16,"title":"Logaritma Denklemi Çözümü","list":{"type":"unordered","items":["Eşitsizliğin çözüm kümesi (-3, -1] kapalı aralığı olduğuna göre, a'nın pozitif değeri 4'tür.","Logaritma fonksiyonlarında denklem her zaman pozitif olmalıdır.","a negatif olursa da problem olmaz çünkü karesini aldığımız için."]},"beginTime":2351,"endTime":2478,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=2351&ask_summarization=1"},{"index":17,"title":"Üstel Fonksiyon Özellikleri","list":{"type":"unordered","items":["Üstel fonksiyon 1/2 üzeri x olarak alınır ve taban 1'den küçük olduğu için azalan bir fonksiyondur.","Ters fonksiyonu logaritma fonksiyonudur.","Grafiği (2, 1/4) noktasından geçer."]},"beginTime":2478,"endTime":2516,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=2478&ask_summarization=1"},{"index":18,"title":"Logaritma Değerleri","list":{"type":"unordered","items":["Logaritma 2 yaklaşık olarak 0,31, logaritma 3 yaklaşık olarak 0,40, logaritma 18 yaklaşık olarak 1,25'tir.","Logaritma 18 değeri 2 logaritma 3 olarak yazılabilir ve yaklaşık 1,25'e eşittir."]},"beginTime":2516,"endTime":2591,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=2516&ask_summarization=1"},{"index":19,"title":"Artan Fonksiyon Özellikleri","list":{"type":"unordered","items":["f(x) = a × 3^bx fonksiyonu artan olduğuna göre, b > 0 şeklinde olmalıdır.","Fonksiyonun artan olması için a'nın da pozitif olması gerekir.","a × b > 0 şeklinde bir sonuç elde edilir."]},"beginTime":2591,"endTime":2694,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=2591&ask_summarization=1"},{"index":20,"title":"Doğrusal Noktalar ve Logaritma","list":{"type":"unordered","items":["KLM noktaları doğrusaldır ve KL = log2(x-3), LM = 1, KM = log15(x+5) olarak verilmiştir.","Logaritma özellikleri kullanılarak denklem çözülür ve x = 7 olarak bulunur."]},"beginTime":2694,"endTime":2772,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=2694&ask_summarization=1"},{"index":21,"title":"Logaritma Denklemi Çözümü","list":{"type":"unordered","items":["Denklemde k = log5 taban x olarak tanımlanır ve denklem çözülür.","k = 5 olarak bulunur ve x = 5^5 olarak hesaplanır."]},"beginTime":2772,"endTime":2829,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=2772&ask_summarization=1"},{"index":22,"title":"Üçgen ve Açıortay","list":{"type":"unordered","items":["ABC üçgeninde A açıortay, AB = log2 taban x, AC = log√2 taban 4x, BN/NC = 1/3 olduğuna göre x'in değeri 16'dır.","Açıortay kuralı kullanılarak denklem çözülür ve x küp = 16x² bulunur.","x = 0, ancak logaritma tanımsız olduğu için x = 0 olarak kabul edilmez."]},"beginTime":2829,"endTime":2948,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=2829&ask_summarization=1"},{"index":23,"title":"Blok Uzunlukları","list":{"type":"unordered","items":["Farklı uzunlukta üç blok verilmiştir ve en uzun iki blok bitişik vaziyette yan yana konulduğunda uzunluğun 10 birim olduğu ölçülüyor.","Denklem 2^x + 2^x + 1 = 10 olarak yazılır ve çözülür.","En kısa bloğun uzunluğu 5/3 birimdir."]},"beginTime":2948,"endTime":3018,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=2948&ask_summarization=1"},{"index":24,"title":"Nüfus Artış Hızı Problemi","list":{"type":"unordered","items":["Nüfus artış hızı formülü: r = ln(Pt/N) şeklindedir, burada Pt son sayım nüfusu, N bir önceki nüfus sayımı ve r artış hızıdır.","2020 yılında nüfusu 150 bin olan bir şehrin nüfus artış hızı 0,1 olarak tahmin edildiğinde, beş yıl sonraki nüfusu 247.500 olarak hesaplanmıştır."]},"beginTime":3027,"endTime":3169,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=3027&ask_summarization=1"},{"index":25,"title":"Üstel Fonksiyon Problemi","list":{"type":"unordered","items":["f(x) ve g(x) üstel fonksiyonlar verilmiş, f(g(2)) = 1/81 olduğuna göre a değeri 2 olarak bulunmuştur."]},"beginTime":3169,"endTime":3227,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=3169&ask_summarization=1"},{"index":26,"title":"Logaritma ve Trigonometri Problemi","list":{"type":"unordered","items":["t bir gerçek sayı, x = e^y = e^sin(t) olmak üzere verilen eşitliklerden hangisinin t eleman R için geçerli olduğu sorulmuştur.","C şıkkı olan ln(x) + ln(y) = 1 ifadesi trigonometrik özdeşliklerden biri olan sin²(t) + cos²(t) = 1'e eşit olduğu için geçerlidir."]},"beginTime":3227,"endTime":3374,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=3227&ask_summarization=1"},{"index":27,"title":"Değer Kazanma Problemi","list":{"type":"unordered","items":["El dokuması antika halının bugünkü değeri 25.000 TL ve her yıl %10 değer kazandığına göre, 30 yıl sonra fiyatı 25.000 TL × (1,10)^30 TL olarak hesaplanmıştır."]},"beginTime":3374,"endTime":3419,"href":"/video/preview/14267483017070210220?parent-reqid=1771627581056420-5292244347666350424-balancer-l7leveler-kubr-yp-sas-194-BAL&text=67Eftw&t=3374&ask_summarization=1"},{"index":28,"title":"Logaritma Toplamı Problemi","list":{"type":"unordered","items":["Ece matematik dersinde logaritma fonksiyonunun tanımı ve özelliklerini anlatmış, f(x) = log₂x grafiğini çizmiş ve f(1) + f(2) + ... + f(10) toplamının değerini yaklaşık olarak bulmalarını 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