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      <text>6.3.2.1 Simplifying expressions involving logarithms</text>
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      <text><![CDATA[<h3>Simplifying expressions involving logarithms</h3><p>To simplify an expression involving logarithms their laws, given in the previous Key Point, need to be used.</p>
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<h4 class="HELM_example">Example</h4>
<p>Simplify: \(\log_{10}2-\log_{10}4+\log_{10}(4^2)+\log_{10}(\frac{10}{4})\)</p>
<h4 class="HELM_solution">Solution</h4>
<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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