I recently came across this intriguing property of logarithms: $(\log_pq)(\log_rs)=(\log_rq)(\log_ps)$, which is linked to a result known as the "chain rule" for logarithms. This seems to be less well-known than various other properties that crop up in typical questions on the topic, so I would be very interested if anyone could point me to some good (or challenging) problems (logarithmic equations, or otherwise) which make use of this property, as I feel I would benefit from the practice.
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This follows quickly from the change-of-base rule, which is useful to try in any problem involving logs in multiple bases. I don't think it's worth practicing this particular corollary rather than a bunch of problems where change-of-base would be useful. – Mark S. May 14 '17 at 03:38