Template:Qlog 10/doc

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The {{qlog_10}} quasilogarithmic function template returns the (base 10) quasilog of $\scriptstyle x\,$, where $\scriptstyle x\,$ 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}}

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 }}
}}

See also

• {{qlog}} and {{qexp}}
• {{qlog_2}} and {{qexp_2}}
• {{qlog_10}} and {{qexp_10}}
• {{qlog_b}} and {{qexp_b}}

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

• {{arsinh}}