[dkislyuk]

Yes, but such a property was not available to Napier, and from a teaching perspective, it requires understanding exponentials and their characterizations first. Starting from the original problem of how to simplify large multiplications seems like a more grounded way to introduce the concept.

[kccqzy]

From a teaching perspective it goes like this: first we learn additions, and to undo additions we have subtractions; then we learn repeated additions i.e. multiplications, and to undo multiplications we have divisions; finally we learn repeated multiplications, i.e. exponentiation, and to undo exponentiation we have logarithms and roots.

[BobaFloutist]

You see how one of those isn't like the others?

[kccqzy]

You mean we have both logarithms and roots to undo exponentiation? That's because exponentiation is non-commutative.

[BobaFloutist]

Right, I'm not saying it's for no reason, but the asymmetry makes it harder to keep track of which undoes exponentiation in which way.

And logs are frankly more confusing than the other operations because more than anything else they feel like an algebraic expression in the form of an operation. Other operations intuitively feel like a process, whereas logs feel like more like a question.

Maybe that's just because I never learned them super well though, maybe they're not actually that inherently different ¯\_(ツ)_/¯