Template:Qlog/doc

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The {{qlog}} quasilogarithmic function template returns the (base $\scriptstyle e\,$) quasilog of $\scriptstyle x\,$, where $\scriptstyle x\,$ 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}}

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 }}
}}

See also

• {{qexp}}
• {{qexp_2}}
• {{qexp_10}}
• {{qexp_b}}

• {{qlog}} (see also {{arsinh}})
• {{qlog_2}}
• {{qlog_10}}
• {{qlog_b}}

• {{exp}}
• {{exp_2}}
• {{exp_10}}
• {{exp_b}}

• {{log}}
• {{log_2}}
• {{log_10}}
• {{log_b}}