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Is there any rule for powers so that i can compare which one is greater without actually calculating? For example

54^53 and 53^54  23^26 and 26^23 3^4 and 4^3 (very simple but how without actually calculating) 
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    In my case (GRE preparation), yes it is.2010-12-31

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If $a\gt b\gt e , b^a\gt a^b$. To see this, take logs. You want to compare $a \ln b$ with $b \ln a$. $\ln$ rises slowly, so the larger multiplier wins.

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    Or just paste the columns into your favorite spreadsheet, take the log of the first entry, multiply by the exponent, use copy down to get all the rows, and ask for the maximum. Spreadsheets are very powerful tools.2011-01-01