In number theory (e.g., Ivić 2003), the symbol is commonly used to mean the nested logarithm (also called the repeated logarithm or iterated logarithm), where is thenatural logarithm.

Care must be taken based on context as to when the notation denotes the logarithm to base and when it means the-nestednatural logarithm.

The plots above show,, and in the complex plane.

The penchant for formulas and bounds containing a profusion of nested logarithms has led to the following joke. What sound does a drowning analytic number theorist make? A: log log log log... (Havil 2003, p. 115).

See also

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More things to try:

• antilogarithm
• binary logarithm
• 125 * 216 * 343

References

Ivić, A. "On a Problem of Erdős Involving the Largest Prime Factor of." 5 Nov 2003.http://arxiv.org/abs/math.NT/0311056.

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Cite this as:

Weisstein, Eric W. "Nested Logarithm."FromMathWorld--A Wolfram Resource.https://mathworld.wolfram.com/NestedLogarithm.html

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