You can think about division like this: to calculate a/b, subtract b from a again and again until you reach 0. The number of times you subtracted is a/b.
Similarly, you can think of log the same way: to calculate logb(a), divide a by b again and again until you reach 1. The number of times you divided is logb(a).
So iterated logarithm is the next level: to calculate log*b(a), take logb of a again and again until you reach 1, and count the number of times.
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