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Let $x\in\mathbb R$ and suppose that $2^x,3^x$ and $5^x$ are all integers. Does it imply that $x$ is also necessarily an integer?

I read somewhere that the answer is "Yes" and a proof is known, but I haven't seen a proof and was not able to prove it myself. Could you please help me to find a proof?

OlegK
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  • see http://math.stackexchange.com/questions/1087841/existence-of-x-such-that-2x-a-3x-b-5x-c-for-some-integers-a-b-c/1087922#1087922 – Will Jagy Jan 10 '15 at 20:42

1 Answers1

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See MO

It follows from the Six Exponentials Theorem. Apparently.

Community
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Myself
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  • see http://math.stackexchange.com/questions/1087841/existence-of-x-such-that-2x-a-3x-b-5x-c-for-some-integers-a-b-c/1087922#1087922 – Will Jagy Jan 10 '15 at 20:44