Template:Log b

The following documentation is located at Template:Log b/doc. [<Edit> Template:Log b/doc]
[⧼Purge⧽ Template:Log b]

The {{log_b}} mathematical function template returns the base $\scriptstyle b\,$ logarithm of $\scriptstyle x\,$, where $\scriptstyle x\,$ and $\scriptstyle b,\,b\,\neq \,1,\,$ are positive real numbers.

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|9|0}}
{{log_b|9|1}}
{{log_b|i|3}}
{{log_b|-1|3}}
{{log_b|0|3}}

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 }}
}}

See also

• {{log}} or {{log_e}} or {{ln}}
• {{log_2}}
• {{log_10}}
• {{log_b}}