3. Let $f(x)$ be a monotonic function defined on the interval $(0,+\infty)$. If for any $x \in(0,+\infty)$, we have
$$
f\left(f(x)-2 \log _{2} x\right)=4,
$$

then the solution set of the inequality $f(x)<6$ is $\qquad$
3. $\{x \mid 0<x<4\}$.

From the problem, we know there exists a positive constant $c$, such that $f(c)=4$, and for any $x \in(0,+\infty)$, we have
$$
\begin{array}{l}
f(x)-2 \log _{2} x=c . \\
\text { When } x=c \text {, we have } \\
f(c)=2 \log _{2} c+c=4,
\end{array}
$$

By monotonicity, we know this equation has a unique solution $c=2$.
Thus, $f(x)=2 \log _{2} x+2$.
From $f(x)<6 \Rightarrow 2 \log _{2} x+2<6 \Rightarrow 0<x<4$.