6. Define an operation $*$ on the set of positive real numbers, with the rule: when $a \geqslant b$, $a * b=b^{a}$; when $a<b$, $a * b=b^{2}$. According to this rule, the solution to the equation $3 * x$ $=27$ is $\qquad$ .
$$
\begin{array}{l}
6 . \quad 3, \quad 3 \sqrt{3} \\
\text { If } \quad 3 \geqslant x, \text { then } 3 * x=x^{3}, \\
\because \quad 27=3^{3}, \\
\therefore \quad x=3 . \\
\text { If } \quad 3<x, \text { then } 3 * x=x^{2}, \\
\because \quad 27=(\sqrt{27})^{2}, \\
\therefore \quad x=\sqrt{27}=3 \sqrt{3} .
\end{array}
$$

Therefore, the solutions to the equation $3 * x=27$ are $3, 3 \sqrt{3}$.