Example 1 If $\log _{a} \frac{2}{3}<1$, then the range of values for $a$ is
If $a>1, \log _{a} \frac{2}{3}<1=\log _{a} a \Rightarrow a>1$; if $0<a<1, \log _{a} \frac{2}{3}<1=\log _{a} a \Rightarrow 0<a<\frac{2}{3}$. Therefore, $a \in\left(0, \frac{2}{3}\right) \cup(1,+\infty)$.