Please find attached problem and my work.

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Originally Posted by Veronica1999 Please find attached problem and my work. The integers with rational logs to the base 8 are all of the form for some natural number . CB

How do I prove that log(base8)6 has an irrational value? I can split this into log(base8)2 + log(base8)3 = 1/3 + ?

Originally Posted by Veronica1999 How do I prove that log(base8)6 has an irrational value? I can split this into log(base8)2 + log(base8)3 = 1/3 + ? Proof by contradiction. Assume it is rational. From unique factorization, this is impossible - a contradiction. QED.

Last edited by elemental; Dec 1st 2010 at 01:28 PM. Reason: formatting

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