log^{*}(`n`) is the number of times you need to apply log to `n` to get a number < 1 (although since it's only ever used for complexity analysis, you can use any other constant instead of 1; 2 also seems popular).

If we take logarithms to base 2, log^{*} is 1 in the range [1,2), 2 in the range [2,4), 3 in the range [4,16), 4 in the range [16,65536), 5 in the range [65536,2^{65536}). An `n` for which log^{*}(`n`)=6 is unimaginable huge: considerably larger than 10^{18000}(!)