Can You Solve These Simultaneous Equations? Most Students Get Stuck!

In this video, I solve the simultaneous equations log₂(x) + log₄(y) = 3 and x + y = 65 step by step, showing how to handle logarithms with different bases and combine them smoothly with algebraic equations. We rewrite log₄(y) in base 2, simplify the expression using log laws, and then use substitution to reduce the system to a single equation that can be solved cleanly without guesswork. This tutorial is ideal for high school students, exam candidates, and math enthusiasts who want to strengthen their understanding of logarithmic equations, change of base, and problem-solving techniques commonly tested in exams and math competitions. TIMESTAMPS 0:00 – Introduction to the simultaneous log equations 0:16 – Changing log base 4 to base 2 (change of base formula) 0:45 – Evaluating log₂(4) using exponent rules 1:29 – Rewriting the equation using log₂ only 1:45 – Removing fractions by multiplying through by 2 2:10 – Applying the power rule of logarithms 2:36 – Combining logs into a single expression 3:01 – Converting the log equation into x²y = 64 3:22 – Solving the system with substitution (y = 65 - x) 3:52 – Forming the cubic equation in x 4:47 – Testing values to find a root of the cubic 5:32 – Using synthetic division method to factor the cubic 6:58 – Reducing the problem to a quadratic equation 7:49 – Solving the quadratic equation by completing the square method 9:26 – Simplifying the square root expression 10:15 – Rejecting invalid solutions using log domain rules 10:40 – Finding the valid x-values 11:01 – Calculating corresponding y-values 12:07 – Final solutions to the simultaneous equations 12:28 – Conclusion and recap Don’t forget to like 👍, subscribe    / @nonsomaths  , and hit the notification bell for more math tips and tricks! #matholympiad #mathtutorial #algebra