Basic Examples
Basic Examples
IteratedLog is the inverse of tetration (repeated exponentiation):
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3
A slightly larger input shows a step-like jump in the value of :
IteratedLog
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4
Make a table of the iterated logarithm of the first 50 integers:
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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}
Scope
Scope
The logarithmic base can be any real number greater than 1:
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5
Applications
Applications
Plot the iterated logarithm for different logarithmic bases:
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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:
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π
π
π