Exponential function not simplified by FullSimplify?

Question

I'm trying to understand why the first expression doesn't simplify while the second does: FullSimplify[a^q <= 1, {0 < a < 1, q > 0}] FullSimplify[q Log[a] <= 0, {0 < a < 1, q > 0}] Aren't these expressions equivalent under the supplied assumptions?

mimuller · Answer

I ended up using this workaround with Reduce instead. Not super pretty, but at least it shows that the algebra is correct. Applied to this example,

assum = {0 < a < 1, q > 0};
FullSimplify[Reduce[And@@ assum && a^q <= 1], assum]

I will wait a bit before accepting this answer in case anyone else has a more elegant approach, but didn't want you to go through the pain of typing out something that already has an answer elsewhere.

Exponential function not simplified by FullSimplify?

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