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Problem of the Day #10: Rational Logs March 29, 2011

Posted by Arjun in : potd , trackback

Given that $a$, $b$, $x$, and $y$ are positive integers, and $a+b = 10$, find the number of ordered pairs $(a,b)$ such that: $$ a^{5\log_2x} = b^{\log_{32}y}$$ where the quotient of $\log x$ and $\log y$ is rational.
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