Which of the numbers $99^{100}$ & $100^{99}$ is the larger? Solve without using logarithms.
Which of the numbers $99^{100}$ and $100^{99}$ is the larger one?
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$\begingroup$
inequality
arithmetic
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62Why do I have to solve it? Even more, why do *I* have to solve it without using logarithms? – 2012-01-28
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6Python: `99**100 > 100*99 == True` – 2012-01-29
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0@nightcracker: Was that a typo??! – 2012-01-29
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0@cardinal: Actually yes, but it still gives you the answer (it returns `False` :P) – 2012-01-29
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0@nightcracker: Except that it's true both with and without the typo, which indicates there's actually a second typo...or Python's doing something a little strange. – 2012-01-29
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3Why all the upvotes? Maybe I should ask a similar (yet abstractly non-duplicate) question... – 2012-01-29
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0@TheChaz: This question is currently at the top of the list of "hot questions" on the SE network. – 2012-01-29
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9-1 This question has showed absolutely no effort whatsoever. @TheChaz I don't get the upvotes either. – 2012-01-29
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5@cardinal: I should explain why @nightcracker's Python returns False. Python allows chained comparisons (`1 <= x < 9`), so it was interpreting `99**100 > 100**99 == True` as one of these. True has an integer comparison value of 1, so this is really `99**100 > 10**99 == 1`, which is false. `99**100 > 100**99` and `(99**100 > 10**99) == True` both return True as you'd expect. – 2012-01-29
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0@cardinal: Thanks for the insight. It's not the end of the world, but sure reinforces the asking of "un-researched" questions. – 2012-01-29
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0@DSM: Thanks. I don't use python really. In the interim, I saw that both of your latter examples worked and then tried `10 > 1 == True` and `10 > 2 == True`. The difference in returned values allowed me to deduce what must be happening. There must be some good reason they decided to allow this in the language specification, but it still strikes me as odd and, as in this case, error-prone. – 2012-01-29
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6No one has explicitly said that the question is simply rude. Michael, using the imperative when asking for a favor will not pay in the long run. – 2012-01-29
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0@TheChaz: More likely, it reinforces the asking of questions that seem "amazing" and "hard" to the (even pretty technically oriented) person with an average math background, but that have several fairly simple and elegant answers. – 2012-01-29
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1@cardinal the reason why that's allowed is because chained expressions simplify a lot of things, while explicitly comparing booleans to True or False is something you shouldn't generally need to do anyway as `if condition == True:` is more verbose than `if condition:` for no good reason. – 2012-01-29
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0in irb: `99**100 > 100**99 #=> true` – 2012-01-30
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0Beronulli inequality kills this problem indeed ! :D – 2012-10-23
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0I love this question, not because of the question, but the vast variety of answers you give (well you all give the same answer) but many of you have completely different methods, and I just love that about math. – 2014-09-09