How do we use logs for multiplication?

Compare this to the fractions method in the prior blog article.

How is the thinking with respect to logs similar to that of the multiplication with fractions approximation?

How did they develop the idea of logs for multiplication?

Was it from this fractions as approximation method?

Or vice versa?

How about using exponents?

27 * 33 = exp(log 27) * exp(log 33)

How could this lead to the multiplication with fractions approximation method of the previous blog article?

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## About New Math Done Right

Author of Pre-Algebra New Math Done Right Peano Axioms. A below college level self study book on the Peano Axioms and proofs of the associative and commutative laws of addition.
President of Mathematical Finance Company. Provides economic scenario generators to financial institutions.