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What is greater: e^pi or pi^e? Six ways to solve this w/o a calculator
- Millennium 13y agoI don't know how you'd prove this, but is it not true that for any real numbers, if 2 <= x < y, then y^x < x^y? Again, I don't know how exactly to prove this, so I could be wrong. But this seems like the most intuitive way to solve something like this: e < pi, so pi^e < e^pi.
- dalke 13y agoIt is not true: >>> x = 2.1 >>> y = 2.2 >>> y**x < x**y False >>> x = 9.0 >>> y = 10.0 >>> y**x < x**y True
- Millennium 13y agoOh, OK then. Good to know. Thanks.