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.
\[
y(x)=\;^a\!\log x,
\]
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.