HMMT 2007 A8

Let $A:=\mathbb{Q} \backslash\{0,1\}$ denote the set of all rationals other than 0 and 1. A function $f: A \rightarrow \mathbb{R}$ has the property that for all $x \in A$,

$$f(x)+f\left(1-\frac{1}{x}\right)=\log |x|$$

Compute the value of $f(2007)$.