SEC2_BM · Algebra · ALG.LOG

Logarithms and logarithm laws

Intuition

Understand first, compress later.

Algebra describes structures generally: a symbol stands for a number, while the rules remain the same.

Switch representations

Mapping between two setsf: A → B — neither injective nor surjective

domain Acodomain Bthe assignment fnot hit

Every element of A has exactly one arrow leaving it — that is what makes f a function. Two elements of A are sent to the same element of B (2 and 3 ↦ b), so f is not injective. Nothing maps onto c, d in B, so f is not surjective.

Formal view

You can logarithms and logarithm laws when you can recognise the underlying objects, select valid rules and check each step for equivalence or logical implication.

Why does it work?

This skill sits on a prerequisite network. If a step is unstable, repair the missing prerequisite instead of merely doing more items of the same type.