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Question

what is difference between log*log n and log(log*n)?

Answer 1

In computer science, the iterated logarithm of n, written log* n (usually read "logstar"), is the number of times the logarithm function must be iteratively applied before the result is less than or equal to 1.

x                              lg* x

(−∞, 1]                        0

(1, 2]                          1

(2, 4]                          2

(4, 16]                        3

(16, 65536]                 4

(65536, 2⁶⁵⁵³⁶]           5

Let n=16 then

log*log n = log*log 16 = log*(4) =2

log(log*n) = log(log*16) = log(3) = 1.5849 approximately = 2