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      <text>4.2.9 (Simplifying logs)</text>
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      <text><![CDATA[<p>We often wish to simplify an expression involving logarithms. In order to do this we use the log laws above in order to combine logs.</p>
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<h3>Example</h3>
<p>Simplify: \(\log_{10}2-\log_{10}4+\log_{10}(4^2)+\log_{10}(\frac{10}{4})\).</p>

<h3>Solution</h3>
<p>The third term \(\log_{10}(4^2)\) simplifies to \(2\log_{10}4\) and the last term \(\log_{10}\left(\dfrac{10}{4}\right)=\log_{10}10-\log_{10}4=1-\log_{10}4\). So the given expression equals</p>
<p>\[\log_{10}2-\log_{10}4+2\log_{10}4+1-\log_{10}4 = \log_{10}2+1.\]</p>]]></text>
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