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Template:Log b/doc
From OeisWiki
The {{log_b}} mathematical function template returns the base logarithm of , where and are positive real numbers.
Contents
Usage
- {{log_b|a positive real number|a positive real number distinct from 1 (base)}}
or
- {{log_b|a positive real number|base = a positive real number distinct from 1 (base)}}
Valid input
- A positive real number as first argument, a positive real number distinct from 1 as second argument (base).
Examples
Examples with valid input
Code Result {{log_b|0.5|2}} -1 {{log_b|1|3}} 0 {{log_b|1.5|base = 1.5}} 1 {{log_b|256|4}} 4 {{log_b|216|6}} 3 {{log_b|216|1/6}} -3 {{log_b|512|8}} 3 {{log_b|10^40|100}} 20 {{log_b|e^pi|e}} 3.1415926535898 {{log_b|pi^e|pi}} 2.718281828459 {{log_b|10^15|base = {{Golden ratio}}}} 71.774579501725 {{log_b|{{Golden ratio}}-1|base = {{Golden ratio}}}} -0.99999999999998 {{log_b|{{Golden ratio}}+1|base = {{Golden ratio}}}} 2
Examples with invalid input (returns an error message)
Code Result {{log_b|9|-3}} Log_b error: Second argument (base) must be a positive real number distinct from 1 {{log_b|9|0}} Log_b error: Second argument (base) must be a positive real number distinct from 1 {{log_b|9|1}} Log_b error: Second argument (base) must be a positive real number distinct from 1 {{log_b|i|3}} Log_b error: First argument must be a positive real number {{log_b|-1|3}} Log_b error: First argument must be a positive real number {{log_b|0|3}} Log_b error: First argument must be a positive real number
Code
{{ifnum| {{{1|not a number}}} | {{#ifexpr: ({{{1}}}) > 0 | {{ifnum| {{{base|{{{2|not a number}}}}}} | {{#ifexpr: ( ({{{base|{{{2}}}}}}) > 0 ) and ( ({{{base|{{{2}}}}}}) != 1 ) | {{#expr: ln ({{{1}}}) / ln ({{{base|{{{2}}}}}}) }} | {{error| Log_b error: Second argument (base) must be a positive real number distinct from 1 }} }} | {{error| Log_b error: Second argument (base) must be a positive real number distinct from 1 }} }} | {{error| Log_b error: First argument must be a positive real number }} }} | {{error| Log_b error: First argument must be a positive real number }} }}