<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>4.2.19 (Change of base to 10 and e)</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Re-express \(\log_{{@aa@}} {@bb@}\) using base \(10\) and base \(e\).</p><p> Enter <code>lg</code> for logs base \(10\), and <code>ln</code> for natural logs. </p>
<ul style="list-style-type:none;">
<li><p>Base \(10\) </p>
<p>\(\log_{{@aa@}} {@bb@} = \) [[input:ans1]] [[validation:ans1]] [[feedback:prt1]]</p></li>
<li><p>Base \(e\) </p>
<p>\( \log_{{@aa@}} {@bb@} = \) [[input:ans2]] [[validation:ans2]] [[feedback:prt2]]</p></li>
<li><p>Now, use your calculator to determine the value of  \(\log_{{@aa@}} {@bb@}\).</p>
<p> \(\log_{{@aa@}} {@bb@} = \) [[input:ans3]] [[validation:ans3]] (Round up and enter \(4\) decimal places. If the answer has less than \(4\) decimal places, then enter zero(s) at the end.) [[feedback:prt3]]</p></li>
</ul>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>Recall the formula for converting logarithms from one base to another 
\[ \log_a b = \dfrac{\log_p b}{\log_p a}. \]</p>
<p>(a) Applying the above formula for \(a = {@aa@}, b ={@bb@} \) and \(p = 10\), we get
\[ \log_{{@aa@}} {@bb@} = \dfrac{\log_{10} {@bb@}}{\log_{10}{@aa@}}.\]</p>
<p>(b) Applying the same formula for \(a = {@aa@}, b={@bb@}\) and \(p = e\), we get
\[ \log_{{@aa@}} {@bb@} = \dfrac{\ln {@bb@}}{\ln{@aa@}}.\]</p>
<p>(c) Note that \(\log_{{@aa@}}{@bb@}\) cannot be determined directly on your calculator since logs to base \({@aa@}\) are not available, but it can be found by changing to base \(10\) or base 
\(e\).</p>
<p>Using logs base \(10\) on your calculator, we get \[ \log_{{@aa@}} {@bb@} = \dfrac{\log_{10} {@bb@}}{\log_{10}{@aa@}} = {@ta3@}.\]</p>
<p>Alternatively, using logs base \(e\) on your calculator, we get \[ \log_{{@aa@}} {@bb@} = \dfrac{\ln {@bb@}}{\ln{@aa@}} = {@ta3@}.\]</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2020081700</text>
    </stackversion>
    <questionvariables>
      <text>aa:rand(5)+20;
bb:rand(6)+2;
ta3:decimalplaces(float(ln(bb)/ln(aa)),4);
simp:false;
ta1:lg(bb)/lg(aa);
ta2:ln(bb)/ln(aa);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\(log_{{@aa@}} {@bb@} = {@ta1@} = {@ta2@} = {@ta3@} \)</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
    <multiplicationsign>none</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
    <isbroken>0</isbroken>
    <variantsselectionseed/>
    <input>
      <name>ans1</name>
      <type>algebraic</type>
      <tans>ta1</tans>
      <boxsize>7</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords>[[BASIC-ALGEBRA]],+</forbidwords>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>3</showvalidation>
      <options/>
    </input>
    <input>
      <name>ans2</name>
      <type>algebraic</type>
      <tans>ta2</tans>
      <boxsize>7</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords>[[BASIC-ALGEBRA]],+</forbidwords>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>3</showvalidation>
      <options/>
    </input>
    <input>
      <name>ans3</name>
      <type>numerical</type>
      <tans>dispdp(ta3,4)</tans>
      <boxsize>7</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords>[[BASIC-ALGEBRA]],log,ln,lg</forbidwords>
      <allowwords/>
      <forbidfloat>0</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>3</showvalidation>
      <options>maxdp:4,mindp:4</options>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
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      <feedbackstyle>1</feedbackstyle>
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        <text/>
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        <tans>ta1</tans>
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    </prt>
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        <sans>ans2</sans>
        <tans>ta2</tans>
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        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
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        <truenextnode>-1</truenextnode>
        <trueanswernote>prt2-1-T</trueanswernote>
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          <text/>
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        <falseanswernote>prt2-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <prt>
      <name>prt3</name>
      <value>1.0000000</value>
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      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
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      <node>
        <name>0</name>
        <description/>
        <answertest>NumDecPlaces</answertest>
        <sans>ans3</sans>
        <tans>ta3</tans>
        <testoptions>4</testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt3-1-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt3-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
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    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ta1</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>ta2</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>dispdp(ta3,4)</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt2-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt3</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt3-1-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ta2</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>ta1</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>ev(ta3+1,simp)</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt2-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt3</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt3-1-F</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
