Binary logarithm - Revision history

FloraC at 10:17, 19 March 2026

2026-03-19T10:17:32Z

← Older revision		Revision as of 10:17, 19 March 2026
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	{{Wikipedia}}		{{Wikipedia}}
	The '''binary logarithm''', also called '''dual logarithm''' or '''logarithm base two''' (symbols: '''log<sub>2</sub>''', '''lb''', or '''ld''') of a value ''n'' is the power to which 2 is raised to obtain ''n''. ~~It is part~~ of ~~the conversion formula for~~ [[frequency ratio]] ~~to interval~~ size in [[cent]]s.		The '''binary logarithm''', also called '''dual logarithm''' or '''logarithm base two''' (symbols: '''log<sub>2</sub>''', '''lb''', or '''ld''') of a value ''n'' is the power to which 2 is raised to obtain ''n''. The binary logarithm of a [[frequency ratio]] measures its size in [[2/1\|octave]]s. [[Interval size measure]]s proportional to the octave, such as the [[cent]], can be found by multiplying the size in octaves by a constant.

	You can calculate the binary logarithm of ''n'' using the identity:		You can calculate the binary logarithm of ''n'' using the identity:

2026-03-18T12:51:13Z

Rework

← Older revision		Revision as of 12:51, 18 March 2026
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	{{Wikipedia~~\| Binary logarithm~~ }}		{{Wikipedia}}
	The ~~symbols~~ '''~~log2~~''', '''lb''', or '''ld''' ~~are used for the~~ '''~~binary logarithm~~''', ~~also called~~ '''~~dual logarithm~~''' or '''~~logarithm base two~~'''.~~{{clear}}~~		The '''binary logarithm''', also called '''dual logarithm''' or '''logarithm base two''' (symbols: '''log<sub>2</sub>''', '''lb''', or '''ld''') of a value ''n'' is the power to which 2 is raised to obtain ''n''. It is part of the conversion formula for [[frequency ratio]] to interval size in [[cent]]s.

	== ~~Log2~~ of the first primes ==		You can calculate the binary logarithm of ''n'' using the identity:

			$$ \log_2(n) = \ln(n) / \ln(2) $$

			== Binary logarithms of the first primes ==
	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	\|-		\|-
	! ~~[[Prime]]~~		! ''p''
	! ~~Log2 prime~~		! log<sub>2</sub>''p''
	\|-		\|-
	\| 2		\| 2
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	\|}		\|}

	~~You can calculate the binary logarithm of ''n'' using the identity:~~

	~~$$ \log_2(n) = \ln(n) / \ln(2) $$~~

	~~[[Category:Math]]~~
	[[Category:Elementary math]]		[[Category:Elementary math]]
	[[Category:Terms]]		[[Category:Terms]]

	~~{{Todo\| improve synopsis }}~~

2026-03-18T12:36:12Z

FloraC moved page Log2 to Binary logarithm: Follow Wikipedia

← Older revision	Revision as of 12:36, 18 March 2026
(No difference)

2025-09-04T13:09:28Z

← Older revision		Revision as of 13:09, 4 September 2025
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	{{Wikipedia\| Binary logarithm }}		{{Wikipedia\| Binary logarithm }}
	The symbols '''log2''', '''lb''' or '''ld''' are used for the '''binary logarithm''', also called '''dual logarithm''' or '''logarithm base two'''.		The symbols '''log2''', '''lb''', or '''ld''' are used for the '''binary logarithm''', also called '''dual logarithm''' or '''logarithm base two'''.{{clear}}

	== Log2 of the first primes ==		== Log2 of the first primes ==

	{\| class="wikitable center-all"		{\| class="wikitable center-all"
			\|-
	! [[Prime]]		! [[Prime]]
	! Log2 prime		! Log2 prime

2025-09-04T06:57:17Z

Adopt the Wikipedia box and misc. cleanup

← Older revision		Revision as of 06:57, 4 September 2025
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	The symbols '''log2''', '''lb''' or '''ld''' are used for the '''~~[[Wikipedia: Binary logarithm\|~~binary logarithm]]''', also called '''dual logarithm''' or '''logarithm base two'''.		{{Wikipedia\| Binary logarithm }}
			The symbols '''log2''', '''lb''' or '''ld''' are used for the '''binary logarithm''', also called '''dual logarithm''' or '''logarithm base two'''.

	== Log2 of the first primes ==		== Log2 of the first primes ==
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	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	! [[Prime]]		! [[Prime]]
	! Log2 ~~Prime~~		! Log2 prime
	\|-		\|-
	\| 2		\| 2
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	\|}		\|}

	You can calculate the binary logarithm of n ~~like this~~:		You can calculate the binary logarithm of ''n'' using the identity:

	~~log2~~(n) = ln(n)/ln(2)		$$ \log_2(n) = \ln(n) / \ln(2) $$

	[[Category:Math]]		[[Category:Math]]
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	[[Category:Terms]]		[[Category:Terms]]

	{{~~todo~~\| improve synopsis }}		{{Todo\| improve synopsis }}

2022-01-20T12:27:16Z

2021-05-06T07:07:22Z

Cleanup

← Older revision		Revision as of 07:07, 6 May 2021
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	The symbols '''log2''', '''lb''' or '''ld''' are used for the '''[~~http~~:~~//en.wikipedia.org/wiki/Binary_logarithm~~ binary logarithm]''', also called '''dual logarithm''' or '''logarithm base two'''.		The symbols '''log2''', '''lb''' or '''ld''' are used for the '''[[Wikipedia: Binary logarithm\|binary logarithm]]''', also called '''dual logarithm''' or '''logarithm base two'''.

	== Log2 of the first primes ==		== Log2 of the first primes ==

	{\| class="wikitable"		{\| class="wikitable center-all"
	! [[~~prime~~]]		! [[Prime]]
	! ~~log2 prime~~		! Log2 Prime
	\|-		\|-
	\| 2		\| 2
	\| 1		\| 1.000000000
	\|-		\|-
	\| 3		\| 3
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	[[Category:Practical help]]		[[Category:Practical help]]
	[[Category:Terms]]		[[Category:Terms]]
	~~[[Category:Todo:~~improve synopsis]]
			{{todo\| improve synopsis }}

2020-12-04T22:44:58Z

← Older revision		Revision as of 22:44, 4 December 2020
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	[[Category:Math]]		[[Category:Math]]
	[[Category:Practical help]]		[[Category:Practical help]]
	[[Category:~~Term~~]]		[[Category:Terms]]

	[[Category:Todo:improve synopsis]]		[[Category:Todo:improve synopsis]]

2020-06-12T14:17:49Z

simplified, added/bolded redirect lemma(s)

← Older revision		Revision as of 14:17, 12 June 2020
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	The symbols '''log2''', '''lb''' or '''ld''' are used for the '''[http://en.wikipedia.org/wiki/Binary_logarithm binary logarithm]''', also called ''dual logarithm''.		The symbols '''log2''', '''lb''' or '''ld''' are used for the '''[http://en.wikipedia.org/wiki/Binary_logarithm binary logarithm]''', also called '''dual logarithm''' or '''logarithm base two'''.

	==Log2 of the first ~~[[prime_numbers\|~~primes]]==		== Log2 of the first primes ==

	{\| class="wikitable"		{\| class="wikitable"
			! [[prime]]
			! log2 prime
	\|-		\|-
	! \| ~~prime~~		\| 2
	! \| ~~log2 prime~~		\| 1
	\|-		\|-
	\| ~~\| 2~~		\| 3
	\| \| 1		\| 1.584962501
	\|-		\|-
	\| ~~\| 3~~		\| 5
	\| ~~\| 1~~.~~584962501~~		\| 2.321928095
	\|-		\|-
	\| ~~\| 5~~		\| 7
	\| \| 2.~~321928095~~		\| 2.807354922
	\|-		\|-
	\| ~~\| 7~~		\| 11
	\| ~~\| 2~~.~~807354922~~		\| 3.459431619
	\|-		\|-
	\| ~~\| 11~~		\| 13
	\| \| 3.~~459431619~~		\| 3.700439718
	\|-		\|-
	\| ~~\| 13~~		\| 17
	\| ~~\| 3~~.~~700439718~~		\| 4.087462841
	\|-		\|-
	\| ~~\| 17~~		\| 19
	\| \| 4.~~087462841~~		\| 4.247927513
	\|-		\|-
	\| ~~\| 19~~		\| 23
	\| \| 4.~~247927513~~		\| 4.523561956
	\|-		\|-
	~~\| \| 23~~		\| 29
	~~\| \| 4.523561956~~		\| 4.857980995
	\|-
	\| \| 29
	\| \| 4.857980995
	\|}		\|}

	You can calculate the binary logarithm of n like this		You can calculate the binary logarithm of n like this:

			log2(n) = ln(n)/ln(2)

			[[Category:Howto]]
			[[Category:Math]]
			[[Category:Practical help]]
			[[Category:Term]]

	~~log2(n) = ln(n)/ln(2)~~		[[Category:Todo:improve synopsis]]
	[[Category:~~howto]]~~
	~~[[Category:math]]~~
	~~[[Category:practical_help]]~~
	~~[[Category~~:~~term~~]]

2018-07-17T00:00:00Z