This One Log Equation Will Test Everything You Know About Logs!

Are you struggling with logarithmic equations? I'd like to help you with that. In this video, I solve the tricky logarithmic equation logₓ(8) − log₄ₓ(8) = log₂ₓ(16), step by step, using smart transformations and the fundamental laws of logarithms. This problem tests your understanding of log bases, change of base formulas, and how to manipulate logarithmic expressions in creative ways to reveal elegant relationships. It’s a perfect challenge for high school students, A-level learners, and math enthusiasts preparing for competitive exams or Olympiad-level problem-solving. You’ll learn not only how to solve it efficiently but also how to think deeply about the structure of logarithmic equations — making your grasp of logs, indices, and exponents even stronger. Logarithm Identities Used in this Video Change of Base Formula:  logₐ(b) = log_c(b) / log_c(a) Product Law:  logₐ(mn) = logₐ(m) + logₐ(n) Power Law:  logₐ(mⁿ) = n·logₐ(m) Base–Power Law (special identity):  logₐ(aⁿ) = n Base Raised to a Power Formula:  logₐⁿ(b) = (1/n)·logₐ(b) Don’t forget to like 👍, subscribe    / @nonsomaths  , and hit the notification bell for more math tips and tricks! #matholympiad #mathtutorial #algebra