Math Olympiad Question, Beautiful Exponential Equation. Can you solve and prove?

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In This video, you will learn how to solve nice exponential equations. It is a math Olympiad question.
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Комментарии
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No way this is an Olympiad question. It is too easy and typical. The "algoritmic" solution is: 256^(-a) is a strictly decreasing function for positive a; a is a strictly increasing function for the same domain. Thus if the equation has a solution, it is unique. Clearly a=1/4 is a solution, thus it is the only one.

vladpetre
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Is it really Olympiad question，it is simple.

huijunjin
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It is nice to know that the limit of x^x is 1 not 0 when x tends to be 0.

SmartAgriculturers