Math Olympiad Problem | Challenging Algebra Problem |How to solve System of Equation |3^x-3^y=-6318

In this video, I will be teaching how to solve this equation in math Olympiad problem. I will be solving this algebraic problem step-by-step so that you won't miss any step. The problem is find m and n from 3^x-3^y=-6318

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[GodbornNoven]

very brilliant. But I feel as though it would have been a bit too difficult if you didn't know the factors of that

[diamonddudeygo]

My problem with this solution is, though it arrives at the correct answer, it's not rigorous.

Even if 3^x is odd and (1 - 3^c) is even, there is no guarantee that (1 - 3^c) doesn't have 3 as a factor. You need to try out every possible value of x between 0 and 5, and even though 5 is the only one that yields an integer result, you don't know that beforehand and you'd need to check in order for this solution to be rigorous.

[deeppandey]

Simple method, convert -6318 in form of subtraction of powers of 3 and then compare, u would get the same ans

[yesveryprofesionalnameyes]

Nice! Although the "proof" that 3^x is odd at 2:50 doesn't really hold. Easy to see with some basic modular arithmetic but can't really use two specific examples as proof. I get that this is not really the point of that conclusion, but it can be misleading and probably should have been proven in the actual olympiad.

[wasimvillidad]

This not the only solution - e.g. x = log₃(217²/4), y = log₃(269²/4).

[agahozcan]

I would just up the factors until I get sth on the 6 thousands and subtract the result from that tbh. I know when the number Is too great It wouldn't be feasible, but I also think that writing It like 243.26 Is also not really practical.

[mluine]

not easy to see behind 6318 the product 243 *26 ... if you don't know this information you're stopped ... thanks for posting tis video!!