Manuals/calci/LBSTAR

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LBSTAR (Number)


  • is any real number.

Description

  • This function shows the iterated logarithm of the given number with the base 2.
  • In , is any real number.
  • 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. LBSTAR(6) = 3
  2. LBSTAR(300) = 4
  3. LBSTAR(67230) = 5

Related Videos

Iterated Logarithm

See Also


References