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      <text>6.4.1.1 Introduction</text>
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      <text><![CDATA[<h3>The logarithmic function
</h3><p style="text-align: left;">Recall the operation of taking logarithms which reverses the operation of exponentiation.
\[\qquad  \text{If}\ a&gt;0 \ \text{and}\ a\ne 1\ \ \text{then}\qquad x=a^y\qquad\text{implies}\qquad y=\log_ax\]
In this quiz we consider the log function in more detail. We shall concentrate only on the functions \(\log x\) (i.e. to base \(10\)) and \(\ln x\) (i.e. to base \(e\)). The functions \(y=\log x\) and \(y=\ln x\) have similar characteristics. We can never choose \(x\) as a negative number since \(10^y\) and \(e^y\) are each always positive. The graphs of \(y=\log x\) and \(y=\ln x\) are shown in the figure below.</p><p style="text-align: center;"><img src="@@PLUGINFILE@@/6.4.1%20fig.svg" alt="logarithmic and exponential functions figure" class="img-responsive atto_image_button_text-bottom" width="327" height="239"> <span class="math display"></span></p>
<p style="text-align: center;">Logarithmic and exponential functions</p>
<p>From the graphs we see that both functions are one-to-one so each has an inverse - the inverse function of \(\log_ax\) is \(a^x\). Let us do this for logs to base \(10\).</p>]]></text>
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