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I actually prefer the straightforward log is an inverse of exponents. It's more intuitive that way because I automatically can understand 10^2 * 10^3 = 10^5. Hence if you are using log tables, addition makes sense. I didn't need an essay to explain that.

Take logs, add 2 + 3 = 5 and then raise it back to get 10^5.

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This is how I've always taught logarithms to students I've tutored. I photocopy a table of various powers of ten, we use it in all sorts of ways to solve problems, and then I sneakily present an "inverse power" problem where they need to make the lookup backwards.

Almost every student gets it right away, and then I tell them looking up things backwards in the power table is called taking a logarithm.

That's how I mentally processed them when first learning them years ago. Doing operations on x and y with log(x) = y in the background somehow felt far less intuitive than thinking about 10^y = x.

I really enjoyed this author's work, BTW. Just spent several hours reading the entire first five chapters or so. What an excellent refresher for high school math in general.

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