document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=412677>Question 412677</A>: <I><SPAN STYLE=\"word-break: break-all;\"> log base 3 of 31\r<BR>\n" );
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document.write( "So far I got log 3 (15.5)+ log 3 (2)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #289813 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=289813\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C+%2831%29%29 ALIGN=MIDDLE  ALT=\"log%283%2C+%2831%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I assume you are supposed to figure out a decimal approximation for this log. (If not, repost it and explain what the problem says for you to do.)<br><BR>\n" );
document.write( "What you did was correct but it did not get you any closer to an answer.<br><BR>\n" );
document.write( "There are two ways to figure out a logarithm. Some logarithms can be found \"by hand\". For example, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C+%2816%29%29 ALIGN=MIDDLE  ALT=\"log%284%2C+%2816%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents the exponent for 4 that results in 16. This exponent we know. It is 2. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C+%2816%29%29 ALIGN=MIDDLE  ALT=\"log%284%2C+%2816%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2.<br><BR>\n" );
document.write( "For logarithms where you can't figure out the right exponent you must use your calculator. Your expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C+%2831%29%29 ALIGN=MIDDLE  ALT=\"log%283%2C+%2831%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents the exponent on a 3 that results in 31. This cannot be done without a calculator because the power of 3 that results in 31 is not well known.<br><BR>\n" );
document.write( "Unfortunately calculators do not have buttons for base 3 logarithms. In order to use our calculators we must change the base of the logarithm, using the change of base formula, to a base your calculator \"knows\", like base 10 or base e (aka ln). The change of base formula is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29 ALIGN=MIDDLE  ALT=\"log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Using this pattern on your expression we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C+%2831%29%29+=+log%28%2831%29%29%2Flog%28%283%29%29 ALIGN=MIDDLE  ALT=\"log%283%2C+%2831%29%29+=+log%28%2831%29%29%2Flog%28%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C+%2831%29%29+=+ln%2831%29%2Fln%283%29 ALIGN=MIDDLE  ALT=\"log%283%2C+%2831%29%29+=+ln%2831%29%2Fln%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Believe it or not, both of these equations will give the same result. I will leave it up to you to pick one, use your calculator (or computer calculator program) to find the two logarithms and then divide.<br><BR>\n" );
document.write( "P.S. In response to your comment about being without a calculator...<ul><li>You need a calculator <i>only</i> if you need/want a decimal approximation of the answer. Otherwise<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C+%2831%29%29+=+log%28%2831%29%29%2Flog%28%283%29%29 ALIGN=MIDDLE  ALT=\"log%283%2C+%2831%29%29+=+log%28%2831%29%29%2Flog%28%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C+%2831%29%29+=+ln%2831%29%2Fln%283%29 ALIGN=MIDDLE  ALT=\"log%283%2C+%2831%29%29+=+ln%2831%29%2Fln%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "would be the preferred answer because they are exactly correct.</li><li>You obviously have access to a computer. Most computers have a calculator program on them. If you are using Windows you will probably find it under<BR>\n" );
document.write( "Start -> Programs -> Accessories<BR>\n" );
document.write( "If not, then try<BR>\n" );
document.write( "Start -> Run...<BR>\n" );
document.write( "and type in \"calc\" (without the quotes) followed by the Enter key.<BR>\n" );
document.write( "Once you start the calculator program, click on the \"View\" menu and select \"Scientific\". This should change the display so that it includes more buttons, including log and ln! </SPAN>\n" );
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