Binary logarithm: Difference between revisions

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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''.
{{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''. 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.  


==Log2 of the first [[prime_numbers|primes]]==
You can calculate the binary logarithm of ''n'' using the identity:


{| class="wikitable"
$$ \log_2(n) = \ln(n) / \ln(2) $$
 
== Binary logarithms of the first primes ==
{| class="wikitable center-all"
|-
|-
! | prime
! ''p''
! | log2 prime
! log<sub>2</sub>''p''
|-
|-
| | 2
| 2
| | 1
| 1.000000000
|-
|-
| | 3
| 3
| | 1.584962501
| 1.584962501
|-
|-
| | 5
| 5
| | 2.321928095
| 2.321928095
|-
|-
| | 7
| 7
| | 2.807354922
| 2.807354922
|-
|-
| | 11
| 11
| | 3.459431619
| 3.459431619
|-
|-
| | 13
| 13
| | 3.700439718
| 3.700439718
|-
|-
| | 17
| 17
| | 4.087462841
| 4.087462841
|-
|-
| | 19
| 19
| | 4.247927513
| 4.247927513
|-
|-
| | 23
| 23
| | 4.523561956
| 4.523561956
|-
|-
| | 29
| 29
| | 4.857980995
| 4.857980995
|}
|}


You can calculate the binary logarithm of n like this
[[Category:Elementary math]]
 
[[Category:Terms]]
log2(n) = ln(n)/ln(2)
[[Category:howto]]
[[Category:math]]
[[Category:practical_help]]
[[Category:term]]

Latest revision as of 10:17, 19 March 2026

English Wikipedia has an article on:

The binary logarithm, also called dual logarithm or logarithm base two (symbols: log2, 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 octaves. Interval size measures 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:

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

Binary logarithms of the first primes

p log2p
2 1.000000000
3 1.584962501
5 2.321928095
7 2.807354922
11 3.459431619
13 3.700439718
17 4.087462841
19 4.247927513
23 4.523561956
29 4.857980995
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