Given $a>0, a \neq 1$, the range of real numbers $k$ that allows the equation $\log _{a}(x-a k)=\log _{a}^{2}\left(x^{2}-a^{2}\right)$ to have a solution is $\qquad$.
7. $(-\infty,-1) \cup(0,1)$.

From the problem, we know $\log _{a}(x-a k)=\frac{1}{2} \log _{c}\left(u^{2}-a^{2}\right)$, which gives $x \cdots a k=\sqrt{x^{2}-a^{2}}$. Therefore, by combining the graphical and numerical analysis, the range of values for $k$ is $(-\infty,-1) \cup(0,1)$.