Binary logarithm: Difference between revisions

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VisualWikitext

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-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{Wikipedia}}
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+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.
-: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2012-03-23 04:19:38 UTC</tt>.<br>
-: The original revision id was <tt>313880170</tt>.<br>
-: The revision comment was: <tt>direct link</tt><br>
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
-<h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The symbol **log2** is often used for the **[[http://en.wikipedia.org/wiki/Binary_logarithm|binary logarithm]]**, also called //dual logarithm//.
-==Log2 of the first [[prime numbers|primes]]==
+You can calculate the binary logarithm of ''n'' using the identity:
-||~ prime ||~ log2 prime ||
-|| 2 || 1 ||
-|| 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 ||
-You can calculate the binary logarithm of n like this
+$$ \log_2(n) = \ln(n) / \ln(2) $$
-log2(n) = ln(n)/ln(2)</pre></div>
+== Binary logarithms of the first primes ==
-<h4>Original HTML content:</h4>
+{| class="wikitable center-all"
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;log2&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The symbol &lt;strong&gt;log2&lt;/strong&gt; is often used for the &lt;strong&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Binary_logarithm" rel="nofollow"&gt;binary logarithm&lt;/a&gt;&lt;/strong&gt;, also called &lt;em&gt;dual logarithm&lt;/em&gt;.&lt;br /&gt;
+|-
-&lt;br /&gt;
+! ''p''
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Log2 of the first primes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Log2 of the first &lt;a class="wiki_link" href="/prime%20numbers"&gt;primes&lt;/a&gt;&lt;/h2&gt;
+! log<sub>2</sub>''p''
+|-
+| 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
+|}
-&lt;table class="wiki_table"&gt;
+[[Category:Elementary math]]
-    &lt;tr&gt;
+[[Category:Terms]]
-        &lt;th&gt;prime&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;log2 prime&lt;br /&gt;
-&lt;/th&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;3&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1.584962501&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;5&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;2.321928095&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;7&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;2.807354922&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;11&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;3.459431619&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;13&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;3.700439718&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;17&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;4.087462841&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;19&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;4.247927513&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;23&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;4.523561956&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;29&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;4.857980995&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-&lt;/table&gt;
-&lt;br /&gt;
-You can calculate the binary logarithm of n like this&lt;br /&gt;
-&lt;br /&gt;
-log2(n) = ln(n)/ln(2)&lt;/body&gt;&lt;/html&gt;</pre></div>