Difference between revisions of "Manuals/calci/LOGSTAR"
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|(16, 65536] || 4 | |(16, 65536] || 4 | ||
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| − | | (65536, <math>2^65536</math>] ||5 | + | | (65536, <math>2^{65536}</math>] ||5 |
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==Examples== | ==Examples== | ||
Revision as of 12:58, 24 May 2017
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 :
Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\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.
| X | Log*X |
|---|---|
| (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 -\infty} ,1] | 0 |
| (1,2] | 1 |
| (2,4] | 2 |
| (4,16] | 3 |
| (16, 65536] | 4 |
| (65536, 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 2^{65536}} ] | 5 |