Binary logarithm: Difference between revisions
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{{Wikipedia | {{Wikipedia}} | ||
The | 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: | |||
$$ \log_2(n) = \ln(n) / \ln(2) $$ | |||
== Binary logarithms of the first primes == | |||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
! | |- | ||
! | ! ''p'' | ||
! log<sub>2</sub>''p'' | |||
|- | |- | ||
| 2 | | 2 | ||
| Line 39: | Line 43: | ||
|} | |} | ||
[[Category:Elementary math]] | [[Category:Elementary math]] | ||
[[Category:Terms]] | [[Category:Terms]] | ||
Latest revision as of 10:17, 19 March 2026
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 |