若函数$f(x) = \left\{ {\begin{array}{*{20}{c}} {{{\left( {\frac{1}{2}} \right)}^x},\;\,} & {x \ge 4,} \\ {f(x + 1),} & {x < 4,} \\ \end{array}} \right. $, 则$f(\log_23) = $( ).