SL 1.5—Intro to logs

Logarithms are one of the two inverse operations of exponentiation — the other being radicals (roots).

Consider the equation $a^b=c$. Depending on which variable you want to isolate:

• To solve for $a$: use a radical → $a=\sqrt[b]{c}$
• To solve for $b$: use a logarithm → $b={\log }_{a}c$

This relationship between exponential and logarithmic form is the single most important thing to understand about logs — everything else follows from it.