Solve Math Olympiad Simultaneous Log Equations Like a Pro!

Are you struggling with simultaneous logarithmic equations? In this video, I solve three challenging systems of equations involving logarithms and exponents—perfect for advanced high school students, math Olympiad participants, or anyone who enjoys deep problem-solving. First, we tackle the system: log₉(x) + logᵧ(8) = 2 and logₓ(9) + log₈(y) = 8⁄3, using log identities and substitution to simplify. Next, we solve: x^(log₈(y)) + y^(log₈(x)) = 4 and log₄(x) − log₄(y) = 1, by converting and balancing logs and exponents. Finally, we take on: 3^(log x) = 2^(log y) and (2x)^(log 2) = (3y)^(log 3), applying properties of exponents and logs creatively to isolate variables. Follow along as I break each system down step by step with clear reasoning and smart algebraic techniques. 00:00 - Solving the first logarithmic system - log₉(x) + logᵧ(8) = 2 and logₓ(9) + log₈(y) = 8⁄3 14:24 - Solving the exponential-logarithmic hybrid system - x^(log₈y) + y^(log₈x) = 4 and log₄x − log₄y = 1 25:06 - Solving the power-log equation system - 3^(log x) = 2^(log y) and (2x)^(log 2) = (3y)^(log 3) Don’t forget to like 👍, subscribe    / @nonsomaths  , and hit the notification bell for more math tips and tricks! #maths #algebra #matholympiad #logarithmicequations #simultaneousequations