Logarithms provide a way to express large numbers compactly, and iterated logarithm involves taking the log multiple times until the result is less than or equal to 1.
The iterated logarithm is denoted as log*b(x), indicating the number of times you need to take the logarithm base b to reach a value less than or equal to 1.
Implementing the iterated logarithm in Python involves a simple function that iterates the logarithm until the desired condition is met.
Skewes' bounds and Mersenne primes are examples where iterated logarithms are used to determine the number of iterations required to reach a small value.