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 → $b={\log }_{a}c$

Logarithm: For positive values $a$, $c$ with $a\ne 1$, the logarithm base $a$ of $c$ is defined as:
${\log }_{a}c=b⟺a^b=c$
In words: ${\log }_{a}c$ asks "What power must I raise $a$ to in order to get $c$?"

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