Reading a Log

To read a log, turn it into a power question. $\log_{3}\left(81\right)$ asks: which power of 3 gives 81? Multiply 3 by itself and count: 3, 9, 27, 81. That took four 3s, so ${3}^{4} = 81$ and $\log_{3}\left(81\right) = 4$.

A log and a power are two ways to write one fact, so you can always check a log by raising the base to it. If you think $\log_{4}\left(64\right)$ is 3, check it: ${4}^{3} = 64$, so it is.

Base 10 has a shortcut: count the zeros. $\log\left(10000\right) = 4$, because 10000 is 1 followed by four zeros, which is ${10}^{4}$.