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I have a question about Element[]

Element[3/2,Rationals]

True OK

Element[Sqrt@2,Rationals]

False OK

Element[Log[4,32],Rationals]

True OK (because it equals 5/2)

Element[Log[4,33],Rationals]
$$\frac{\log (33)}{\log (4)}\in \mathbb{Q}$$

NOT OK because I should get False

So Element "knows" if something is true but not if it is false
Can anybody explain this?

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    $\begingroup$ from help, under possible issues, it says When domain membership cannot be decided the Element statement remains unevaluated: So Mathematica could not decide. That is what the answer means. Mathematica did not say False. It said I do not know. Which is OK. Even Mathematica sometimes can't solve a problem. $\endgroup$ – Nasser Feb 14 at 2:01
  • $\begingroup$ @Nasser don't you think that Mathematica should be able to answer this kind of question? $\endgroup$ – J42161217 Feb 14 at 2:06
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    $\begingroup$ Please DO NOT use the bugs tag when posting new questions. DO add the bugs tag when you verified someone else's question to be about an actual bug. See the tag description for more info. Please fix the tags on this post. $\endgroup$ – Szabolcs Feb 14 at 7:53
  • $\begingroup$ @Szabolcs Can you please suggest the right tags for this question? What are your thoughts about my question? Finding out if a logarithm is rational or not is pretty easy in maths. Don't you think that Mathematica should be able to deal with such easy problems? $\endgroup$ – J42161217 Feb 14 at 12:57
  • $\begingroup$ I think tagging as symbolic computation is appropriate here. I disagree that this is a bug. Element does not do much on its own, and can't be used for testing. FullSimplify[Element[x,set]] can be, and also does not work here. I would call it a missing feature, but not a bug. $\endgroup$ – Szabolcs Feb 14 at 14:17

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