Math Olympiad Challenge | Can you solve for a, b?👍

A great challenge. Math Olympiad Question
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[@lechaiku]

We can this way also: 2^a - 2^b = 2016 2^a - 2^b = 2048 - 32 2^a - 2^b = 2^11 - 2^5 (the same bases, the same math operation [subtracting], so we can compare terms respectively) 2^a = 2^11------------------------------ 2^b = 2^5 a = 11---------------------------------------b = 5

[@kamilhorvat8290]

In order to get complete solution, you should also provide an argument why there is not any other a,b satisfying the equation. But I'd solve it the same way, since I know powers of two by heart.

[@lechaiku]

@@kamilhorvat8290 This is the shortcut for the students who take an exam, where the time is a crucial factor. But we know that there are two exponential functions, hence each has a one-to-one property. Each x gives only one y, and each y gives only one x. So the conclusion is, that an exponential equations have only one solution.