Originally Posted by

**euphony** I'm supposed to prove that log(*m*)/log(*n*) is rational if and only if there is some integer *k* such that *m* and *n *(which are integers) are powers of *k*.

It's an "if and only if" proof, so there are two parts:

a) Show that the existence of said integer *k* implies that log(*m*)/log(*n*) is rational. I did this, but I don't understand how to do the second part:

b) Show that log(*m*)/log(*n) *being rational implies that there is some integer *k* such that *m* and *n* are powers of *k*.

If log(*m*)/log(*n*) is rational, it can be represented as *a*/*b* where *a* and *b* are integers and *b* is not 0.