若函数$f\left(x\right)=\left\{\begin{array}{ll}-x+6,x\le 2& \\ 3+{\log }_{a}x,x>2& \end{array}\right.(a>0\mathrm{且a}\ne 1)$ 的值域是$[4,+\infty )$ ，则实数$a$ 的取值范围是