# Question #3385d

Dec 25, 2015

$\log$ is a function and therefore we need an argument to talk about it's value.

#### Explanation:

$\log \left(x\right)$ is whatever value $y$ which is required to make ${10}^{y} = x$

$\log \left(1000\right)$ is $3$ since ${10}^{3} = 1000$

The default base for $\log$ as seen above is $10$.
Other bases can be specified as:
$\textcolor{w h i t e}{\text{XXX}} {\log}_{3} \left(x\right)$ which would be the value $y$ needed to make ${3}^{y} = x$
$\textcolor{w h i t e}{\text{XXX}} {\log}_{3} \left(81\right) = 4$ since ${3}^{4} = 81$