For the function $f: \mathbf{k}^{+} \rightarrow \mathbf{R}^{-}$, which satisfies: for any positive real number $x$, $f(3 x)=3 f(x)$, and $f(x)=1-|x-2|$, $1 \leqslant x \leqslant 3$. Then the smallest positive number $x$ such that $f(x)=f(2001)$ is $\qquad$
8. 429 .

By the given conditions, it is easy to know that for $k \geqslant 0, k \in \mathbf{Z}$, when $3^{2} \leqslant x \leqslant 2 \times 3^{k}$, $f(x)=x-3^{k}$; when $2 \times 3^{\nu} \leqslant x \leqslant$ $3^{4+1}$, $f(x)=3^{k-1}-x$. Since $2 \times 3^{5}<2001<3^{7}$, we have $f(2001)=3^{7}-2001=186$. Also, $3^{4}<$