Manuals/calci/LOGSTAR

LOGSTAR (Number,Base)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Number} is any real number.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Base} base value of the log.

Description

This function shows the iterated logarithm of the given number.
In Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle LOGSTAR (Number,Base)} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Number} is any real number.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Base} 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 :

${\begin{cases}0&ifn\leq 1\\1+log*(logn)&ifn>1\\\end{cases}}$

The relation between Log star and Super logarithm is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle log*n=[slog_e(n)]} for positive real numbers.
Also for negative real numbers ,log star value is 0,whereas Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [slog_e(-x)]= -1} 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.