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		<id>https://matte1b.mathonline.se/index.php?action=history&amp;feed=atom&amp;title=1.5_L%C3%B6sning_5b</id>
		<title>1.5 Lösning 5b - Versionshistorik</title>
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		<updated>2026-08-21T18:03:26Z</updated>
		<subtitle>Versionshistorik för denna sida på wikin</subtitle>
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	<entry>
		<id>https://matte1b.mathonline.se/index.php?title=1.5_L%C3%B6sning_5b&amp;diff=26675&amp;oldid=prev</id>
		<title>Taifun den 7 juli 2015 kl. 15.01</title>
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				<updated>2015-07-07T15:01:03Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
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				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Äldre version&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Versionen från 7 juli 2015 kl. 15.01&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Rad 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Rad 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;:&lt;/del&gt;:&amp;lt;math&amp;gt;\&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;begin{align} (2^x + 2^{x-1}) &lt;/del&gt;\&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;cdot {2 &lt;/del&gt;\&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;over 3}&lt;/del&gt;\&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;; &amp;amp; &lt;/del&gt;= \&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;; 32&amp;#160; \qquad \; | \; &lt;/del&gt;\cdot &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;{3 &lt;/del&gt;\&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;over 2}&amp;#160; &lt;/del&gt;\\&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:&amp;lt;math&amp;gt; &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;4&lt;/ins&gt;\&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;,800&lt;/ins&gt;\&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;,000&lt;/ins&gt;\&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;,000&amp;#160; &lt;/ins&gt;\&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, &lt;/ins&gt;= \&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, 48 &lt;/ins&gt;\cdot &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;100&lt;/ins&gt;\&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;,000&lt;/ins&gt;\&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;,000 &lt;/ins&gt;\&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, &lt;/ins&gt;= \&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, &lt;/ins&gt;48 \cdot &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;10&lt;/ins&gt;\&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;,&lt;/ins&gt;^&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;8 &lt;/ins&gt;\&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, &lt;/ins&gt;= \&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, 4,8 &lt;/ins&gt;\cdot &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;10&lt;/ins&gt;\&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;,&lt;/ins&gt;^&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;9 &lt;/ins&gt;&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;&amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; 2^x + 2^{x-1} &amp;amp; &lt;/del&gt;= \&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;; &lt;/del&gt;48 &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;&amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; \\&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;&amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160;  2^x + 2^x &lt;/del&gt;\cdot &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;2^{-1} &amp;amp; = \; 48&amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160;  \&lt;/del&gt;\&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;&amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160;  2&lt;/del&gt;^&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;x &lt;/del&gt;\&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;cdot (1+{1\over 2}) &amp;amp; &lt;/del&gt;= \&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;; 48&amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160;  \\&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;&amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; {3 \over 2} &lt;/del&gt;\cdot &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;2^x &amp;amp; = &lt;/del&gt;\&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;; 48&amp;#160; \qquad \; | \; \cdot {2 \over 3}\\&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;&amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; 2&lt;/del&gt;^&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;x &amp;amp; = \; 32&amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160;  \\&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;&amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; 2^x &amp;amp; = \; 2^5&amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160;  \\&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;&amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; x &amp;amp; = \;&amp;#160; 5&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;&amp;#160; &amp;#160; &amp;#160; &amp;#160; \end{align} &lt;/del&gt;&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Taifun</name></author>	</entry>

	<entry>
		<id>https://matte1b.mathonline.se/index.php?title=1.5_L%C3%B6sning_5b&amp;diff=3085&amp;oldid=prev</id>
		<title>Taifun den 10 mars 2011 kl. 13.43</title>
		<link rel="alternate" type="text/html" href="https://matte1b.mathonline.se/index.php?title=1.5_L%C3%B6sning_5b&amp;diff=3085&amp;oldid=prev"/>
				<updated>2011-03-10T13:43:46Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;Ny sida&lt;/b&gt;&lt;/p&gt;&lt;div&gt;::&amp;lt;math&amp;gt;\begin{align} (2^x + 2^{x-1}) \cdot {2 \over 3}\; &amp;amp; = \; 32  \qquad \; | \; \cdot {3 \over 2}  \\&lt;br /&gt;
                                            2^x + 2^{x-1} &amp;amp; = \; 48                         \\&lt;br /&gt;
                                   2^x + 2^x \cdot 2^{-1} &amp;amp; = \; 48                         \\&lt;br /&gt;
                                 2^x \cdot (1+{1\over 2}) &amp;amp; = \; 48                         \\&lt;br /&gt;
                                    {3 \over 2} \cdot 2^x &amp;amp; = \; 48  \qquad \; | \; \cdot {2 \over 3}\\&lt;br /&gt;
                                                      2^x &amp;amp; = \; 32                         \\&lt;br /&gt;
                                                      2^x &amp;amp; = \; 2^5                       \\&lt;br /&gt;
                                                        x &amp;amp; = \;  5&lt;br /&gt;
        \end{align} &amp;lt;/math&amp;gt;&lt;/div&gt;</summary>
		<author><name>Taifun</name></author>	</entry>

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