Why is it difficult to "undo" exponentiation?
A viewer asked me recently to explain the difference between logs and roots. We can think of either logs or roots as, in some sense, "inverses" of exponentiation, but right off the bat, that's weird, because why would we need two different inverses? If we need to undo addition, we just subtract. If we need to undo multiplication, we just divide. But all of a sudden for exponential equations, we need two separate inverse operations?
This video is an excerpt from my longer answer, which is the related video above, and can be found on my channel @polymathematic . I hope you'll watch!
#RootsVsLogs #ExponentiationBasics #LogarithmsExplained