AUSTRIAN-POLISH 1989 Problem 7

Functions $f_0, f_1,f_2,...$ are recursively defined by $f_0(x) = x$ and $f_{2k+1} (x) = 3^{f_{2k}(x)}$ and $f_{2k+2} = 2^{f_{2k+1}(x)}$ , $k = 0,1,2,...$ for all $x \in R$ . Find the greater one of the numbers $f_{10}(1)$ and $f_9(2)$ .