Logarithmic functions

Definition: A function of the form
$$y(x)=\;^a\!\log x,$$
where $a$ ($a\neq 1$) is a positive number is called a logarithmic function with base $a$.

Remark: The function $y(x)=\;^a\!\log x$ is not defined for $a=1$.

Extra explanation: Every logarithmic function $y(x)$ has one zero: $x=1$.

Example: $y(x)=\;^2\!\log x$ is an example of a logarithmic function.