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style="margin-bottom: 10px"><i class="fa fa-send"></i> Feedback</button> </div> </div> <div class="col-md-9" id="main-column"> <h1 class="page_title"> 1.5 Exponents and Logarithms <a href="#" class="mark-page-favorite pull-right" data-pid="1998" title="Mark as favorite" onclick="return false;"><i class="fa fa-star-o"></i></a> </h1> <ol class="breadcrumb"> <li><a href="../../../mathsapplications.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../1057/number-and-algebra.html">Number and Algebra</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">1.5 Exponents and Logarithms</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 30 minutes"><i class="fa fa-clock-o"></i> 30'</span> </ol> <article id="main-article"> <div class="intro-card"> <div class="bg-cover" style="background-image: url('/media/mathsapplications/powers.png');"> </div> <img src="../../powers-1.png" style="display: none"> <div class="content"> <p class="theading">Exponents</p> <p class="text">The exponents of a number tell us how many times the number has been multiplied. Understanding these well, and being able to apply the laws of exponents will help us when sketching graphs, using calculus, and working with very large or very small numbers. </p> </div> </div> <div class="panel panel-has-colored-body panel-turquoise"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <p><span id="docs-internal-guid-fe8981b2-7fff-c3b0-0f29-5660053639d1"></span></p> <p dir="ltr"><span id="docs-internal-guid-fe8981b2-7fff-c3b0-0f29-5660053639d1">In this unit you should learn to…</span></p> <ul> <li>Use the basic laws of exponents</li> <li>Understand the concepts of logarithms</li> <li>Evaluate logarithms and exponents using technology</li> </ul> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <h3>Learn about it</h3> <p>The following is a series of videos that will help you understand, learn about and review this sub-topic.</p> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p> 1. Laws of Exponents</p> </div> </div> <div class="panel-body"> <p>What are the main laws of exponents and why are they useful?</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/666476499?h=1028b9bd47&badge=0&autopause=0&player_id=0&app_id=58479"></iframe></div> <script src="../../../api/player.js"></script></div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p> 2. Concept of a Logarithm</p> </div> </div> <div class="panel-body"> <p>What are logarithms?</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/666484496?h=4ca17b8a5f&badge=0&autopause=0&player_id=0&app_id=58479"></iframe></div> <script src="../../../api/player.js"></script></section> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>3. e and ln</p> </div> </div> <div class="panel-body"> <p>More about the exponential and the natural logarithm</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/666492196?h=83ef5ab038&badge=0&autopause=0&player_id=0&app_id=58479"></iframe></div> <script src="../../../api/player.js"></script></section> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>4. Using the GDC</p> </div> </div> <div class="panel-body"> <p>A quick look at how to use the GDC to solve problems with exponents and logarithms. </p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/666501998?h=42008a5fb9"></iframe></div> <p><a href="https://vimeo.com/666501998">Recording #97</a> from <a href="https://vimeo.com/user95446532">Rebecca Baker</a> on <a href="https://vimeo.com">Vimeo</a>.</p> </section> </div> </div> </div> </div> <div class="panel panel-has-colored-body panel-violet"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Summary</p> </div> </div> <div class="panel-body"> <div id="carousel-274" class="dynamic-gallery carousel slide" data-id="274"><div class="carousel-inner" role="listbox"><div class="item active"><a class="fancy" href="../../../std-galleries/15-274/151-laws-of-exponents-1.png" data-fancybox="gallery-274" title="" data-caption=""><img alt="" src="../../../std-galleries/15-274/151-laws-of-exponents-1.png"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-274/151-laws-of-exponents-2.png" data-fancybox="gallery-274" title="" data-caption=""><img alt="" src="../../../std-galleries/15-274/151-laws-of-exponents-2.png"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-274/151-laws-of-exponents-3.png" data-fancybox="gallery-274" title="" data-caption=""><img alt="" src="../../../std-galleries/15-274/151-laws-of-exponents-3.png"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-274/152-concept-of-a-logarithm-1.png" data-fancybox="gallery-274" title="" data-caption=""><img alt="" src="../../../std-galleries/15-274/152-concept-of-a-logarithm-1.png"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-274/152-concept-of-a-logarithm-2.png" data-fancybox="gallery-274" title="" data-caption=""><img alt="" src="../../../std-galleries/15-274/152-concept-of-a-logarithm-2.png"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-274/153-e-and-ln-1.png" data-fancybox="gallery-274" title="" data-caption=""><img alt="" src="../../../std-galleries/15-274/153-e-and-ln-1.png"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-274/153-e-and-ln-2.png" data-fancybox="gallery-274" title="" data-caption=""><img alt="" src="../../../std-galleries/15-274/153-e-and-ln-2.png"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-274/153-e-and-ln-3.png" data-fancybox="gallery-274" title="" data-caption=""><img alt="" src="../../../std-galleries/15-274/153-e-and-ln-3.png"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-274/153-e-and-ln-4.png" data-fancybox="gallery-274" title="" data-caption=""><img alt="" src="../../../std-galleries/15-274/153-e-and-ln-4.png"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-274/153-e-and-ln-5.png" data-fancybox="gallery-274" title="" data-caption=""><img alt="" src="../../../std-galleries/15-274/153-e-and-ln-5.png"></a></div></div><a class="left carousel-control" href="#carousel-274" role="button" data-slide="prev"><i class="fa fa-fw fa-chevron-left"></i></a><a class="right carousel-control" href="#carousel-274" role="button" data-slide="next"><i class="fa fa-fw fa-chevron-right"></i></a></div><ol class="std-carousel-indicators"><li data-index="0"><img title="Click to view" src="../../../std-galleries/15-274/151-laws-of-exponents-1-thumb128.jpg"><li><li data-index="1"><img title="Click to view" src="../../../std-galleries/15-274/151-laws-of-exponents-2-thumb128.jpg"><li><li data-index="2"><img title="Click to view" src="../../../std-galleries/15-274/151-laws-of-exponents-3-thumb128.jpg"><li><li data-index="3"><img title="Click to view" src="../../../std-galleries/15-274/152-concept-of-a-logarithm-1-thumb128.jpg"><li><li data-index="4"><img title="Click to view" src="../../../std-galleries/15-274/152-concept-of-a-logarithm-2-thumb128.jpg"><li><li data-index="5"><img title="Click to view" src="../../../std-galleries/15-274/153-e-and-ln-1-thumb128.jpg"><li><li data-index="6"><img title="Click to view" src="../../../std-galleries/15-274/153-e-and-ln-2-thumb128.jpg"><li><li data-index="7"><img title="Click to view" src="../../../std-galleries/15-274/153-e-and-ln-3-thumb128.jpg"><li><li data-index="8"><img title="Click to view" src="../../../std-galleries/15-274/153-e-and-ln-4-thumb128.jpg"><li><li data-index="9"><img title="Click to view" src="../../../std-galleries/15-274/153-e-and-ln-5-thumb128.jpg"><li></li></ol> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test yourself</p> </div> </div> <div class="panel-body"> <div> <h4>Quiz</h4> <p>Practice your understanding on these quiz questions. Check your answers when you are done and read the worked solutions when you get stuck. If you find there are still some gaps in your understanding then go back to the videos above<em>.</em></p> <div class="tib-quiz" data-stats="15-567-1998"><div class="label label-default q-number">1</div><div class="exercise shadow-bottom"><div class="q-question"><p>Find</p><p><span class="math-tex">\({ 5 }^{ -2 }\times { 5 }^{ 5 }\)</span></p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span class="math-tex">\({ 25 }^{ -10 }\)</span></label> </p><p><label class="radio"> <input type="radio"> <span class="math-tex">\({ 25 }^{ 3 }\)</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span class="math-tex">\({ 5 }^{ 3 }\)</span></label> </p><p><label class="radio"> <input type="radio"> <span class="math-tex">\({ 5 }^{ -10 }\)</span></label> </p></div><div class="q-explanation"><p>When the bases are the same, multiply the exponents only.</p><p><span class="math-tex">\({ =5 }^{ (-2+5) }\)</span></p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">2</div><div class="exercise shadow-bottom"><div class="q-question"><p>Simplify</p><p><span class="math-tex">\({ { (2 }^{ 3 }) }^{ 4 }\)</span></p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span><span class="math-tex">\( { 2 }^{ 12 }\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\( { 8 }^{ 4 }\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\( { 16 }^{ 12 }\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\( { 2 }^{ 7 }\)</span></span></label> </p></div><div class="q-explanation"><p>This is equivalent to <span class="math-tex">\({ { 2 }^{ 3 } } \times { { 2 }^{ 3 } } \times{ { 2 }^{ 3 } } \times { { 2 }^{ 3 } } .\)</span> As the bases are the same we can now simply add together the exponents.</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">3</div><div class="exercise shadow-bottom"><div class="q-question"><p>Simplify</p><p><span class="math-tex">\(3{ y }^{ -2 } \)</span></p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span><span class="math-tex">\(\frac { 3 }{ y^2 } \)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(\frac { 1 }{ 9y^2 } \)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(-6x\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(\frac { 1 }{ 3y^2 } \)</span></span></label> </p></div><div class="q-explanation"><p><span class="math-tex">\(3{ y }^{ -2 }=3{ \quad \times \quad y }^{ -2 }\)</span></p><p><span class="math-tex">\({ y }^{ -2 }=\frac { 1 }{ y^2 } \)</span></p><p>Therefore</p><p><span class="math-tex">\({ 3y }^{ -2 }=3\times \frac { 1 }{ y^2 } \)</span></p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">4</div><div class="exercise shadow-bottom"><div class="q-question"><p>If <span class="math-tex">\({ a }^{ 3 }\times { a }^{ 4 }={ a }^{ n }\)</span>, what is <span class="math-tex">\(n\)</span>?</p></div><div class="q-answer"><p>n = <input type="text" style="height: auto;" data-c="7"> <span class="review"></span> </p></div><div class="q-explanation"><p><span class="math-tex">\({ a }^{ m }\times { a }^{ n }={ a }^{ m+n }\)</span></p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">5</div><div class="exercise shadow-bottom"><div class="q-question"><p>If <span class="math-tex">\({ ({ 2p }^{ 3 }) }^{ 2 }=a{ p }^{ n }\)</span>, what are the values of <span class="math-tex">\(a\)</span> and <span class="math-tex">\(n\)</span>?</p></div><div class="q-answer"><p>a = <input type="text" style="height: auto;" data-c="4"> <span class="review"></span></p><p>n = <input type="text" style="height: auto;" data-c="6"> <span class="review"></span></p></div><div class="q-explanation"><p><span class="math-tex">\({ ({ 2p }^{ 3 }) }^{ 2 }={ 2 }^{ 2 }\times { p }^{ 3\times 2 }=4{ p }^{ 6 }\)</span></p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">6</div><div class="exercise shadow-bottom"><div class="q-question"><p>If <span class="math-tex">\({ 5 }^{ -1 } =n\)</span>, what is the value of <span class="math-tex">\(n\)</span>? (<em>Without a calculator</em>)</p></div><div class="q-answer"><p>n = <input type="text" style="height: auto;" data-c="0.2"> <span class="review"></span> </p></div><div class="q-explanation"><span class="math-tex">\({ 5 }^{ -1 }=\frac { 1 }{ { 5 } } =0.2\)</span></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">7</div><div class="exercise shadow-bottom"><div class="q-question"><p>If <span class="math-tex">\({ ({ 3 }^{ 0 }) }^{ -3 }=\frac { m }{ n } \)</span>, what are the values of <span class="math-tex">\(m\)</span> and <span class="math-tex">\(n\)</span>? (<em>Without a calculator</em>)</p></div><div class="q-answer"><p>m = <input type="text" style="height: auto;" data-c="1"> <span class="review"></span> </p><p>n = <input type="text" style="height: auto;" data-c="1"> <span class="review"></span> </p></div><div class="q-explanation"><span class="math-tex">\({ ({ 3 }^{ 0 }) }^{ -3 }={ 1 }^{ -3 }=\frac { 1 }{ { 1 }^{ 3 } } =\frac { 1 }{ 1 } \)</span></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">8</div><div class="exercise shadow-bottom"><div class="q-question"><p>If <span class="math-tex">\({ (\frac { { 9x }^{ 5 } }{ { 4y }^{ 7 } } ) }^{ -3 }=\frac { a{ y }^{ b } }{ m{ x }^{ n } } \)</span>, what are the values of <span class="math-tex">\(a\)</span>, <span class="math-tex">\(b\)</span>, <span class="math-tex">\(m\)</span> and <span class="math-tex">\(n\)</span>?</p></div><div class="q-answer"><p>a = <input type="text" style="height: auto;" data-c="64"> <span class="review"></span> </p><p>b = <input type="text" style="height: auto;" data-c="21"> <span class="review"></span> </p><p>m = <input type="text" style="height: auto;" data-c="729"> <span class="review"></span> </p><p>n = <input type="text" style="height: auto;" data-c="15"> <span class="review"></span> </p></div><div class="q-explanation"><span class="math-tex">\({ (\frac { { 9x }^{ 5 } }{ { 4y }^{ 7 } } ) }^{ -3 }=\frac { 1 }{ { (\frac { { 9x }^{ 5 } }{ { 4y }^{ 7 } } ) }^{ 3 } } =1\times { (\frac { { 4y }^{ 7 } }{ { 9x }^{ 5 } } ) }^{ 3 }=\frac { { ({ 4y }^{ 7 }) }^{ 3 } }{ { ({ 9x }^{ 5 }) }^{ 3 } } =\frac { 64{ y }^{ 21 } }{ 729{ x }^{ 15 } } \)</span></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">9</div><div class="exercise shadow-bottom"><div class="q-question"><p>If <span class="math-tex">\({ (\frac { { 4a }^{ 3 }\times 2{ a } }{ { 12{ a }^{ 4 }\times a } } ) }^{ -3 }=\frac { { ma }^{ n } }{ x{ a }^{ y } } \)</span>, what are the values of <span class="math-tex">\(m\)</span>, <span class="math-tex">\(n\)</span>, <span class="math-tex">\(x\)</span> and <span class="math-tex">\(y\)</span>?</p></div><div class="q-answer"><p>m = <input type="text" style="height: auto;" data-c="1728"> <span class="review"></span> </p><p>n = <input type="text" style="height: auto;" data-c="15"> <span class="review"></span> </p><p>x = <input type="text" style="height: auto;" data-c="512"> <span class="review"></span> </p><p>y = <input type="text" style="height: auto;" data-c="12"> <span class="review"></span> </p></div><div class="q-explanation"><span class="math-tex">\({ (\frac { { 4a }^{ 3 }\times 2{ a } }{ { 12{ a }^{ 4 }\times a } } ) }^{ -3 }=\frac { 1 }{ { (\frac { { 4a }^{ 3 }\times 2{ a } }{ { 12{ a }^{ 4 }\times a } } ) }^{ 3 } } =1\times { (\frac { 12{ a }^{ 4 }\times a }{ { { 4a }^{ 3 }\times 2{ a } } } ) }^{ 3 }={ (\frac { { 12a }^{ 5 } }{ { 8{ a }^{ 4 } } } ) }^{ 3 }=\frac { { { ({ 12a }^{ 5 }) }^{ 3 } } }{ { { (8a }^{ 4 }) }^{ 3 } } =\frac { 1728{ a }^{ 15 } }{ 512{ a }^{ 12 } } \)</span></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">10</div><div class="exercise shadow-bottom"><div class="q-question"><p>If <span class="math-tex">\(\frac { 5 }{ { a }^{ 4 } } \times { 3a }^{ 8 }=m{ a }^{ n }\)</span>, what are the values of <span class="math-tex">\(m\)</span> and <span class="math-tex">\(n\)</span>? </p></div><div class="q-answer"><p>m = <input type="text" style="height: auto;" data-c="15"> <span class="review"></span> </p><p>n = <input type="text" style="height: auto;" data-c="4"> <span class="review"></span> </p></div><div class="q-explanation"><span class="math-tex">\(\frac { 5 }{ { a }^{ 4 } } \times { 3a }^{ 8 }=5{ a }^{ -4 }\times { 3a }^{ 8 }=15{ a }^{ -4+8 }=15{ a }^{ 4 }\)</span></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="totals"><span class="score"></span><button class="btn btn-success btn-block text-center check-total"><i class="fa fa-check-square-o"></i> Check</button></div></div><hr> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Exam Style Questions</p> </div> </div> <div class="panel-body"> <p>The following questions are based on IB exam style questions from past exams. You should print these off (from the document at the top) and try to do these questions under exam conditions. Then you can check your work with the video solution.</p> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 1</p> </div> </div> <div class="panel-body"> <p> </p> <p><meta charset="utf-8"></p> <p dir="ltr"><b id="docs-internal-guid-b91d8884-7fff-43f6-8c7c-2da3269306ea">The population (P) of turtles on a beach after t years is modelled by the formula</b><b> <span class="math-tex">\(P=200\times e^{0.1t}\)</span></b>. </p> <p dir="ltr"><strong>a. Find the number of turtles: </strong></p> <p dir="ltr"><strong>i. Initially</strong></p> <p dir="ltr"><strong>ii. After 3 years</strong></p> <p dir="ltr"><strong>b. The year that the population first exceeds 500. </strong></p> <p dir="ltr"><strong>(4 marks)</strong></p> <p>Video Solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p style="text-align: center"> </p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/669172416?h=6862efc803&badge=0&autopause=0&player_id=0&app_id=58479"></iframe></div> <script src="../../../api/player.js"></script> <p> </p> </section> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p> Question 2</p> </div> </div> <div class="panel-body"> <p><strong>The Richter scale measures the strength of an earthquake. The strength (S) is given by <span class="math-tex">\(S=\log\left(A\right)\)</span>, where A is the amplitude of the wave. </strong></p> <p><strong>a. If the amplitude of the wave is 500, find the strength of the earthquake</strong></p> <p><strong>b. If the strength of the earthquake is 6.5, find the amplitude of the wave</strong></p> <p><strong>c. If the strength of wave increases by 1, what is the change in the amplitude on the seismograph?</strong></p> <p>Video Solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p style="text-align: center"> </p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/669183766?h=afa4d5c09d&badge=0&autopause=0&player_id=0&app_id=58479"></iframe></div> <script src="../../../api/player.js"></script> <p> </p> </section> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"> <div> <p>Question 3</p> </div> </div> <div class="panel-body"> <p>Video Solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> </section> </div> </div> </div> </div> <div class="panel panel-aubergine panel-has-colored-body panel-has-border panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Just For Fun</p> </div> </div> <div class="panel-body"> <div> <p>There are some fascinating properties of the number 'e'. You can learn more about them here: </p> <ul> <li><a href="http://www.youtube.com/watch?v=AuA2EAgAegE">Numberphile video</a></li> <li><a href="http://www.bbc.co.uk/programmes/b04hz49f">Podcast 'in our time'</a></li> </ul> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="page-container panel-self-assessment" data-id="1998"> <div class="panel-heading">MY PROGRESS</div> <div class="panel-body understanding-rate"> <div class="msg"></div> <label class="label-lg">Self-assessment</label><p>How much of <strong>1.5 Exponents and Logarithms</strong> have you understood?</p><div class="slider-container text-center"><div id="self-assessment-slider" class="sib-slider self-assessment " data-value="1" data-percentage=""></div></div> <label class="label-lg">My notes</label> <textarea name="page-notes" class="form-control" rows="3" placeholder="Write your notes here..."></textarea> </div> <div class="panel-footer text-xs-center"> <span id="last-edited" class="mb-xs-3"> 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