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      <text>6.3.1.1 Logarithms</text>
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      <text><![CDATA[<h3>Logarithms</h3>
<p>Logarithms reverse the process of raising a base '\(a\)' to a power '\(n\)'. </p>
<p>As with all exponentials, the base should be a positive number. If \(b=a^n\) then we write \(\log_ab=n\). </p>
<p>Of course, the reverse statement is equivalent: If \(\log_ab=n\), then \(b=a^n\). </p>
<p>The expression \(log_ab=n\) is read: “The log to base \(a\) of the number \(b\) is equal to \(n\)".</p>
<p>The term “log" is short for the word <b>logarithm</b>.</p>
<hr>
<h4 class="HELM_example">Example</h4>
<p>Determine the log equivalents of</p>
<ol class="HELM_parts_inline">
<p></p><li>\(16 = 2^4\)</li>
<li>\(16 = 4^2\)</li>
<li>\(1000 = 10^3\)</li><p></p>
<p></p><li>\(134.896=10^{2.13}\)</li>
<li>\(8.414867=e^{2.13}\)</li><p></p>
</ol>
<h4 class="HELM_solution">Solution</h4>
<ol class="HELM_parts">
<li> Since \(16=2^4\), \(\log_216=4\).</li>
<li> Since \(16=4^2\), \(\log_416=2\).</li>
<li> Since \(1000=10^3\), \(\log_{10}1000=3\).</li>
<li> Since \(134.896=10^{2.13}\), \(\log_{10}134.896=2.13\).</li>
<li> Since \(8.414867=e^{2.13}\), \(\log_e8.414867=2.13\).</li>
</ol>
<h5><b>Summary:</b></h5>
<div class="HELM_keypoint">
<h4>Key Point</h4>
<p>If \(b=a^n\), then \(log_ab=n\).</p>
<p>If \(\log_ab=n\), then \(b=a^n\).</p>
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