$b^n$ where the base $b$ is a positive integer greater than $1$ and the exponent $n$ is a rational number in simplified form. How would one compare (resulting in <, =, or >) two such exponentiations without evaluating the exponentiatoins, and without the use of functions or operations that produce real numbers (e.g., log(), pow(), etc)?
Comparing two exponentiations
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exponentiation
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0As in comparing $b^n$ and $c^m$ ? different bases and different exponents? – 2012-12-28
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1I do not understand what is being asked. Could you please elaborate? What do you mean by compare? – 2012-12-28
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0if $gcd(b,c)=1$ can the two numbers be equal? – 2012-12-28
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2I give an algorithm for exactly this problem in this question: http://math.stackexchange.com/questions/97049/comparing-powers-without-logarithms – 2012-12-28
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0@RustynYazdanpour I don't know. – 2012-12-28