Mathematics for Data Science 1 - W6_L6: Logarithmic functions – change of base theorem

Welcome to Week 6 Lecture 6 of the course "Mathematics for Data Science I" by Profs. Neelesh Upadhye, Madhavan Mukund. Full Course: https://study.iitm.ac.in/ds/course_pages/BSMA1001.html Video Overview This lecture revisits the basics of logarithms and introduces the powerful Change of Base Theorem. We discuss why natural logarithms (ln) and common logarithms (log base 10) are so central in engineering and scientific applications. You’ll see a clear proof of the theorem, and how it allows any logarithm to be rewritten in terms of ln or log, making calculations simpler with a scientific calculator. Practical examples are provided to show how this theorem streamlines solving logarithmic problems across mathematics, calculus, and engineering. About IIT Madras' online Bachelor of Science programme IIT Madras offers four-year BS programmes that aim to provide quality education to all, irrespective of age, educational background, or location. The BS programme has multiple levels, which provide flexibility to students to exit at any of these levels. Depending on the courses completed and credits earned, the learner can receive a Foundation Certificate from IITM CODE (Centre for Outreach and Digital Education), Diploma(s) from IIT Madras, or BSc/BS Degrees from IIT Madras. For more details, visit: https://www.iitm.ac.in/academics/study-at-iitm/non-campus-bs-programmes #logarithms #changeofbase #naturallogarithm #commonlogarithm #logarithmproperties #logbase10 #logbasee #ln #theorem #mathematicalproof #logarithmicfunction #lawsoflogarithms #mathematics #calculus #engineering #datasciencemath #iitmadras #onlinestudy