### Basic Examples

Basic Examples

IteratedLog is the inverse of tetration (repeated exponentiation):

[E^E^E]

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3

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A slightly larger input shows a step-like jump in the value of :

IteratedLog

[E^E^E+1]

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4

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Make a table of the iterated logarithm of the first 50 integers:

Table

[i],{i,0,50}

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{0,0,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3}

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### Scope

Scope

The logarithmic base can be any real number greater than 1:

[Sqrt[2]+1/2,Pi^Pi^Pi]

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5

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### Applications

Applications

Plot the iterated logarithm for different logarithmic bases:

ListLinePlot Table

[i],{i,0,30}, Table

[8,i],{i,0,30}, Table

[20,i],{i,0,30},PlotLegends{"iterated natural log","iterated log base-8","iterated log base-20"}

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### Possible Issues

Possible Issues

IteratedLog will return unevaluated in cases where evaluation might lead to numerical overflow:

[1.3,Pi^Pi^Pi]

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1.3,π

π

π

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