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# Template:Qlog 10/doc

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The {{qlog_10}} quasilogarithmic function template returns the (base 10) quasilog of ${\displaystyle \scriptstyle x\,}$, where ${\displaystyle \scriptstyle x\,}$ is a real number.

## Usage

{{qlog_10|a real number}}

## Valid input

A real number as argument.

## Examples

Examples with valid input

Code Result Comment
{{qlog_10|10^60}} 60
{{qlog_10|10^50}} 50
{{qlog_10|10^40}} 40
{{qlog_10|10^30}} 30
{{qlog_10|10^25}} 25
{{qlog_10|10^20}} 20
{{qlog_10|10^15}} 15
{{qlog_10|10^10}} 10
{{qlog_10|10^5}} 5.0000000000434
{{qlog_10|10}} 1.0042792113563
{{qlog_10|1}} 0.20898764024998
{{qlog_10|10^-1}} 0.021705686457112
{{qlog_10|10^-5}} 2.1714724095219E-6
{{qlog_10|10^-10}} 2.1714725891304E-11
{{qlog_10|10^-15}} 1.9286549331066E-16
{{qlog_10|10^-20}} 0 (underflow)
{{qlog_10|10^-25}} 0 (underflow)
{{qlog_10|10^-30}} 0 (underflow)
{{qlog_10|10^-35}} 0 (underflow)
{{qlog_10|10^-36}} 0 (underflow)
{{qlog_10|10^-37}} 0 (underflow)
{{qlog_10|10^-40}} 0 (underflow)
{{qlog_10|10^-50}} 0 (underflow)
{{qlog_10|10^-60}} 0 (underflow)
{{qlog_10|0}} 0
{{qlog_10|-(10^-60)}} -0 (underflow)
{{qlog_10|-(10^-50)}} -0 (underflow)
{{qlog_10|-(10^-40)}} -0 (underflow)
{{qlog_10|-(10^-37)}} -0 (underflow)
{{qlog_10|-(10^-36)}} -0 (underflow)
{{qlog_10|-(10^-35)}} -0 (underflow)
{{qlog_10|-(10^-30)}} -0 (underflow)
{{qlog_10|-(10^-25)}} -0 (underflow)
{{qlog_10|-(10^-20)}} -0 (underflow)
{{qlog_10|-(10^-15)}} -1.9286549331066E-16
{{qlog_10|-(10^-10)}} -2.1714725891304E-11
{{qlog_10|-(10^-5)}} -2.1714724095219E-6
{{qlog_10|-(10^-1)}} -0.021705686457112
{{qlog_10|-1}} -0.20898764024998
{{qlog_10|-10}} -1.0042792113563
{{qlog_10|-(10^5)}} -5.0000000000434
{{qlog_10|-(10^10)}} -10
{{qlog_10|-(10^15)}} -15
{{qlog_10|-(10^20)}} -20
{{qlog_10|-(10^25)}} -25
{{qlog_10|-(10^30)}} -30
{{qlog_10|-(10^40)}} -40
{{qlog_10|-(10^50)}} -50
{{qlog_10|-(10^60)}} -60

Examples with invalid input (returns an error message)

Code Result
{{qlog_10|i}} Qlog_10 error: Argument must be a real number

## Code

```
<!--{{#expr: {{arsinh|({{{1}}}) / 2}} / ln 10 }}-->{{ifnum| {{{1|NAN}}}
| {{#ifexpr: ({{{1}}}) >= 0
| {{#expr: ln ( (({{{1}}})/2) + ( (({{{1}}})/2)^2 + 1 )^(1/2) ) / ln 10}}
| {{#expr: - ln ( - (({{{1}}})/2) + ( (({{{1}}})/2)^2 + 1 )^(1/2) ) / ln 10}} <!-- Equivalent, but avoids underflow for negative argument -->
}}
| {{error| Qlog_10 error: Argument must be a real number }}
}}

```