# 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.

X | Log*X |
---|---|

(,1] | 0 |

(1,2] | 1 |

(2,4] | 2 |

(4,16] | 3 |

(16, 65536] | 4 |

(65536, ] | 5 |

## Examples

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

## Related Videos

## See Also

## References