A great exponential equation - 3^x=x^9👍

A great challenge. Math Olympiad Question
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[@Arysto-Krzysztof]

Based on the graphs there is second solution x≈1.151. Function x^1/x is not monotonous so you can't just say that it has to be 27. Additionally equation 3^x=x^9 has different domain than your last equation. You can't just raise everything to the power of 1/x without assuming that x is positive, so you have to check what happens when x is negative or 0.

[@abendyman]

But how did you know to put it to the power of ⅓ and 3. It solves it but i dont see where youre getting those numbers without already knowing the solution?

[@sofisofi-gx8te]

he was probably just testing ideas before getting to the solution

[@abendyman]

@sofisofi-gx8te if its a trial and improvement you require the trial and improvement to be shown to show how you solved it. And how is anyone supposed to know that