How to Compare powers without calculating?

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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Is it always $a^b$ vs $b^a$? –  Aryabhata Dec 30 '10 at 20:18
In my case (GRE preparation), yes it is. –  LifeH2O Dec 31 '10 at 18:23

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.
+1,that's nice explanation,but what could be for any $a^b$ and $c^d$ ? –  Quixotic Dec 31 '10 at 10:32