Difference between revisions of "Manuals/calci/SLOG"
Jump to navigation
Jump to search
| Line 11: | Line 11: | ||
*The two exponentiation function powers and exponentials have two inverse functions roots and logarithms,the two tetration functions tetra powers and tetra exponentials have two inverse functions tetra roots and tetra logarithms also called super roots and super logarithms. | *The two exponentiation function powers and exponentials have two inverse functions roots and logarithms,the two tetration functions tetra powers and tetra exponentials have two inverse functions tetra roots and tetra logarithms also called super roots and super logarithms. | ||
*The super-logarithm, written <math>slog_{b}{z}</math> is defined implicitly by | *The super-logarithm, written <math>slog_{b}{z}</math> is defined implicitly by | ||
| − | <math>slog_{b}(b^{z}) = slog_{b}{z}+1 </math> and | + | <math>slog_{b}(b^{z}) = slog_{b}{z}+1 </math> and |
| − | <math> slog_{b}(1) = 0</math> | + | <math> slog_{b}(1) = 0</math> |
| + | |||
| + | ==Examples== | ||
| + | #SLOG(45,5) = 1.534887252451906 | ||
| + | #SLOG(187,3) = 2.3195001328620837 | ||
| + | #SLOG(-342,4) = -2 | ||
| + | |||
| + | ==See Also== | ||
| + | *[[Manuals/calci/LOG| LOG]] | ||
| + | *[[Manuals/calci/SUPERLOGARITHM| SUPERLOGARITHM]] | ||
| + | *[[Manuals/calci/LOGINV| LOGINV]] | ||
| + | |||
| + | ==References== | ||
| + | *[https://en.wikipedia.org/wiki/Super-logarithm Super logarithm] | ||
| + | |||
| + | *[[Z_API_Functions | List of Main Z Functions]] | ||
| + | *[[ Z3 | Z3 home ]] | ||
Revision as of 14:16, 9 May 2017
SLOG (Number,Base)
- is any real number.
- is any positive real number.
is any real number.
is any positive real number.Description
- This function shows the super 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 SLOG(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 the value to find log value.
- 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.
- SLOG is the super-logarithm which is one of the two inverse functions of tetration.
- This is also called Tetra logarithm.
- The two exponentiation function powers and exponentials have two inverse functions roots and logarithms,the two tetration functions tetra powers and tetra exponentials have two inverse functions tetra roots and tetra logarithms also called super roots and super logarithms.
- The super-logarithm, written 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_{b}{z}} is defined implicitly by
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_{b}(b^{z}) = slog_{b}{z}+1 }
and
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_{b}(1) = 0}
Examples
- SLOG(45,5) = 1.534887252451906
- SLOG(187,3) = 2.3195001328620837
- SLOG(-342,4) = -2