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<title>Exponents, Roots and Logarithms</title>
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<h1 class="center">Exponents, Roots and Logarithms</h1>
<p><span class="center"><a href="../exponent.html">Exponents</a>, Roots (such as <a href="../square-root.html">square roots</a>, cube roots etc) and <a href="logarithms.html">Logarithms</a> are all related!</span></p>
<p>Let's start with the simple example of <b>3 &times; 3 = 9</b>:</p>
<table cellpadding="6" border="0" align="center">
<tbody>
<tr>
<td class="larger">3 Squared</td>
<td class="larger">=</td>
<td height="180" valign="top"><img src="images/3-squared-box.svg" alt="3 by 3 squares = 9 squares"></td>
<td class="larger">= 3 &times; 3 = <b>9</b></td>
</tr>
</tbody></table>
<p>Using Exponents we write it as:</p>
<p class="center largest">3<sup>2</sup> = 9</p>
<p>When any of those values are missing, we have a question. And (sadly) a <b>different notation</b>:</p>
<p>&nbsp;</p>
<p class="largest" style="float:left; margin: 0 20px 5px 0;">3<sup>2</sup> = ?</p>
<p>is the <a href="../exponent.html">exponent</a> question "what is 3 squared?": &nbsp; <span class="large">3<sup>2</sup> = 9</span></p>
<p>&nbsp;</p>
<p class="largest" style="float:left; margin: 0 20px 5px 0;">?<sup>2</sup> = 9</p>
<p>is the <a href="../square-root.html">root</a> question "what is the square root of 9?": &nbsp; <span class="large">&radic;9 = 3</span></p>
<p>&nbsp;</p>
<p class="largest" style="float:left; margin: 0 20px 5px 0;">3<sup>?</sup> = 9</p>
<p>is the <a href="logarithms.html">logarithm</a> question "what is log base 3 of 9?": &nbsp; <span class="large"> log<sub>3</sub>(9) = 2</span></p>
<p>&nbsp;</p>
<p>So when you are stuck trying to solve questions with logs, roots&nbsp;or exponents just remember that!</p>
<p>&nbsp;</p>
<p>One more example: </p>
<div class="example">
<p class="center largest">10<sup>3</sup> = 1000 </p>
<p>&nbsp;</p>
<p class="largest" style="float:left; margin: 0 20px 5px 0;">10<sup>3</sup> = ?</p>
<p>"What is 10 cubed?": &nbsp; <span class="large">10<sup>3</sup> = 1000</span></p>
<p>&nbsp;</p>
<p class="largest" style="float:left; margin: 0 20px 5px 0;">?<sup>3</sup> = 1000</p>
<p>"What is the cube root of 1000?": &nbsp; <span class="large">&#x221b;1000 = 10</span></p>
<p>&nbsp;</p>
<p class="largest" style="float:left; margin: 0 20px 5px 0;">10<sup>?</sup> = 1000</p>
<p>"What is log base 10 of 1000?": &nbsp; <span class="large"> log<sub>10</sub>(1000) = 3</span></p>
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<p>&nbsp;</p>
<p>&nbsp;</p>
<div class="related"><a href="../exponent.html">Exponents</a> <a href="index.html">Algebra Index</a></div>
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