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# Template:Qlog

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

## Usage

{{qlog|a real number}}

## Valid input

A real number as argument.

## Examples

Examples with valid input

Code Result Comment
{{qlog|e^60}} 60
{{qlog|e^50}} 50
{{qlog|e^40}} 40
{{qlog|e^30}} 30
{{qlog|e^25}} 25
{{qlog|e^20}} 20
{{qlog|e^15}} 15
{{qlog|e^10}} 10.000000002061
{{qlog|e^5}} 5.0000453968383
{{arsinh|(e^5)/2}} 5.0000453968383 (should equal the one above)
{{qlog|e}} 1.1140014968063
{{qlog|1}} 0.4812118250596
{{qlog|e^-1}} 0.18291797116413
{{arsinh|(e^-5)/2}} 0.0033689671266103 (should equal the one below)
{{qlog|e^-5}} 0.0033689671266103
{{qlog|e^-10}} 2.269996487911E-5
{{qlog|e^-15}} 1.5295116003095E-7
{{qlog|e^-20}} 1.0305767345305E-9
{{qlog|e^-25}} 6.9440009297964E-12
{{qlog|e^-30}} 4.6851411639181E-14
{{qlog|e^-35}} 2.2204460492503E-16
{{qlog|e^-36}} 2.2204460492503E-16
{{qlog|e^-37}} 0 (underflow)
{{qlog|e^-40}} 0 (underflow)
{{qlog|e^-50}} 0 (underflow)
{{qlog|e^-60}} 0 (underflow)
{{qlog|0}} 0
{{qlog|-(e^-60)}} -0 (underflow)
{{qlog|-(e^-50)}} -0 (underflow)
{{qlog|-(e^-40)}} -0 (underflow)
{{qlog|-(e^-37)}} -0 (underflow)
{{qlog|-(e^-36)}} -2.2204460492503E-16
{{qlog|-(e^-35)}} -2.2204460492503E-16
{{qlog|-(e^-30)}} -4.6851411639181E-14
{{qlog|-(e^-25)}} -6.9440009297964E-12
{{qlog|-(e^-20)}} -1.0305767345305E-9
{{qlog|-(e^-15)}} -1.5295116003095E-7
{{qlog|-(e^-10)}} -2.269996487911E-5
{{qlog|-(e^-5)}} -0.0033689671266103
{{arsinh|-(e^-5)/2}} -0.0033689671266103 (should equal the one above)
{{qlog|-(e^-1)}} -0.18291797116413
{{qlog|-1}} -0.4812118250596
{{qlog|-e}} -1.1140014968063
{{arsinh|-(e^5)/2}} -5.0000453968383 (should equal the one below)
{{qlog|-(e^5)}} -5.0000453968383
{{qlog|-(e^10)}} -10.000000002061
{{qlog|-(e^15)}} -15
{{qlog|-(e^20)}} -20
{{qlog|-(e^25)}} -25
{{qlog|-(e^30)}} -30
{{qlog|-(e^40)}} -40
{{qlog|-(e^50)}} -50
{{qlog|-(e^60)}} -60

Examples with invalid input (returns an error message)

Code Result
{{qlog|i}} Qlog error: Argument must be a real number

## Code

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

```