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Welcome to Week 9 Tutorial 1 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 In this tutorial, we solve a logarithmic equation with multiple bases: 3 log_p(9) - 2 log_q(27) = 2 log_(p^-1 q)(81), where p and q are distinct positive real numbers. The task is to prove that either p = q^3 or q = p^3. We break down the equation step by step, applying base-change techniques, exponent rules, and algebraic manipulation. Substitutions are used to simplify the expressions and reveal the relationship between p and q. 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 #logarithm #logarithmicEquation #equationSolving #mathTutorial #logarithms #algebra #mathematics #problemSolving #baseChange #exponents #mathHelp #datasciencemath #iitmadras #onlinestudy
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