### Instruction: Is $f(x) = \log{x} $ an even function, odd function, or neither?

Enter "odd", "even", or "neither".### Response: So we want to know whether $f(x) = \log{x}$ is an even function, odd function, or neither.
Right. To do that, we need to know what those terms mean.
An even function $f(x)$ has the property that $f(-x) = f(x)$.
An odd function $f(x)$ has the property that $f(-x) = -f(x)$.
So for $f(x) = \log{x}$, we have $f(-x) = \log{(-x)}$.
So $f(-x) \neq f(x)$ and $f(-x) \neq -f(x)$.