Manuals/calci/LOGSTAR

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LOGSTAR (Number,Base)


  • is any real number.
  • base value of the log.

Description

  • This function shows the iterated logarithm of the given number.
  • In , is any real number.
  • is the base value of the log.
  • Log star is the number of times the logarithm function must be iteratively applied before the result is less than or equal to 1.
  • The simple definition of the Log star is :

  • The relation between Log star and Super logarithm is for positive real numbers.
  • Also for negative real numbers ,log star value is 0,whereas for positive x.
  • The iterated logarithm varies at slow rate,which is very slow compared with logarithm values.
  • Iterated logarithm values vary not more than 5 with base value 2.
Spreadsheet
X Log*X
(,1] 0
(1,2] 1
(2,4] 2
(4,16] 3
(16, 65536] 4
(65536, ] 5

Examples

  1. LOGSTAR(3) = 1
  2. LOGSTAR(260) = 2
  3. LOGSTAR(5432,3) = 3

See Also


References