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		<title>1.8 Lösning 5a - Versionshistorik</title>
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		<updated>2026-11-05T20:56:23Z</updated>
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	<entry>
		<id>https://wiki.mattekollen.se/index.php?title=1.8_L%C3%B6sning_5a&amp;diff=4192&amp;oldid=prev</id>
		<title>Taifun den 20 april 2011 kl. 15.50</title>
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				<updated>2011-04-20T15:50:17Z</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} \ln\,x                          &amp;amp; = 1 + \ln\,(x-1)  \; &amp;amp; &amp;amp;\;| \; - \ln\,(x-1) \\&lt;br /&gt;
                    \ln\,x - \ln\,(x-1)             &amp;amp; = 1 \; &amp;amp; &amp;amp;: \;\text{Logaritmlag 2 i VL}     \\&lt;br /&gt;
                    \ln\,\left({x \over x-1}\right) &amp;amp; = 1 \; &amp;amp; &amp;amp;\;| \; e\,^{\cdot}  \\&lt;br /&gt;
                                      {x \over x-1} &amp;amp; = e \; &amp;amp; &amp;amp;\;| \; \cdot (x-1)  \\&lt;br /&gt;
                                                  x &amp;amp; = e \cdot (x-1)                         \\&lt;br /&gt;
                                                  x &amp;amp; = e \cdot x - e \;   &amp;amp; &amp;amp;\;| \; + e - x    \\&lt;br /&gt;
                                                  e &amp;amp; = e \cdot x - x \;   &amp;amp; &amp;amp;: \;\text{Bryt ut} \; x \;\text{i HL } \\&lt;br /&gt;
                                                  e &amp;amp; = x \cdot (e - 1) \; &amp;amp; &amp;amp;\;| \; / \; (e-1) \\&lt;br /&gt;
                                                  x &amp;amp; = {e \over e-1} &lt;br /&gt;
      \end{align}&amp;lt;/math&amp;gt;&lt;/div&gt;</summary>
		<author><name>Taifun</name></author>	</entry>

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