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# Template:Log b

The {{log_b}} mathematical function template returns the base ${\displaystyle \scriptstyle b\,}$ logarithm of ${\displaystyle \scriptstyle x\,}$, where ${\displaystyle \scriptstyle x\,}$ and ${\displaystyle \scriptstyle b,\,b\,\neq \,1,\,}$ 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 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 }}
}}

```