3. If the function
$$
f(x)=\log _{a}\left(4 x+\frac{a}{x}\right)
$$

is increasing on the interval $[1,2]$, then the range of values for $a$ is $\qquad$ .
3. $(1,4]$.

Let $g(x)=4 x+\frac{a}{x}$.
According to the problem;
when $0<x<\frac{\sqrt{a}}{2}$, $g(x)$ is a decreasing function, and when $x>\frac{\sqrt{a}}{2}$, $g(x)$ is an increasing function.
Since $g(x)$ is an increasing function on the interval $[1,2]$, we have $\frac{\sqrt{a}}{2} \leqslant 1 \Rightarrow a \leqslant 4$.
Therefore, the range of values for $a$ is $(1,4]$.