3. Given a constant $a>0$ and $a \neq 1$, if the function $f(x)=\log _{a}\left(x^{3}-a x\right)(a>0, a \neq 1)$ is monotonically increasing in the interval $\left(-\frac{1}{2}, 0\right)$, then the range of values for $a$ is $\qquad$ .
3. $\frac{3}{4} \leqslant a0, \forall x \in\left(-\frac{1}{2}, 0\right)$, i.e., $a>x^{2}, \forall x \in\left(-\frac{1}{2}, 0\right)$, so $a>\frac{1}{4}$. Therefore, the necessary and sufficient condition is $\left\{\begin{array}{l}\frac{1}{4}<a \leqslant 1, \\ 3 x^{2}-a \geqslant 0, \forall x \in\left(-\frac{1}{2}, 0\right)\end{array} \therefore \frac{3}{4} \leqslant a<1\right.$.