document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=340247>Question 340247</A>: <I><SPAN STYLE=\"word-break: break-all;\">  I am asked to express in terms of log m and log n\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #243822 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=243822\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I could interpret this in 2 ways.\r<BR>\n" );
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document.write( "The first way would be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28n%2C%28%2810%2Am%29%5E3%29%29 ALIGN=MIDDLE  ALT=\"log%28n%2C%28%2810%2Am%29%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Under that assumption, your answer would be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2A+%28log%28n%2C%28m%29%29+%2B+log%28n%2C%2810%29%29%29 ALIGN=MIDDLE  ALT=\"3+%2A+%28log%28n%2C%28m%29%29+%2B+log%28n%2C%2810%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The second way would be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28n%2C%2810%2Am%5E3%29%29 ALIGN=MIDDLE  ALT=\"log%28n%2C%2810%2Am%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Under that assumption, your answer would be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28n%2C%2810%29%29+%2B+3+%2A+log%28n%2C%28m%29%29 ALIGN=MIDDLE  ALT=\"log%28n%2C%2810%29%29+%2B+3+%2A+log%28n%2C%28m%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The difference is in whether you are taking 10 * m and then raising the result to the 3d power, or you are taking m to the third power and then multiplying the result by 10.\r<BR>\n" );
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document.write( "There are two main concepts at work.\r<BR>\n" );
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document.write( "The first concept is that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%28%28a+%2A+b%29%29+=+log%28%28a%29%29+%2B+log%28%28b%29%29 ALIGN=MIDDLE  ALT=\"log+%28%28a+%2A+b%29%29+=+log%28%28a%29%29+%2B+log%28%28b%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The second concept is that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%28%28a%5Eb%29%29+=+b+%2A+log%28%28a%29%29 ALIGN=MIDDLE  ALT=\"log+%28%28a%5Eb%29%29+=+b+%2A+log%28%28a%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "If you are solving for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+%2A+m%5E3 ALIGN=MIDDLE  ALT=\"10+%2A+m%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then you use the first concept because the letter a represents 10 and the letter b represents m^3.\r<BR>\n" );
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document.write( "If you are solving for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2Am%29%5E3 ALIGN=MIDDLE  ALT=\"%2810%2Am%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then you use the second concept because <BR>\n" );
document.write( "the letter a represents (10*m) and the letter b represents 3.\r<BR>\n" );
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document.write( "Note that the concept used for each piece of the puzzle changes as you progress through the steps of the problem.\r<BR>\n" );
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document.write( "log(10*m^3) becomes log(10) + log(m^3) because a represents 10 and b represents m^3.   The first concept was used.\r<BR>\n" );
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document.write( "now that you have log(10) + log(m^3), then the second part of log(m^3) becomes 3*log(m) because a represents m and b represents 3).  The second concept was used on the second part.\r<BR>\n" );
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document.write( "The first concept was used to break it up into 2 pieces.\r<BR>\n" );
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document.write( "The second concept was used to break the second piece down further.\r<BR>\n" );
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document.write( "The log of (10 * m^3) is not the same as the log of ((10*m)^3).\r<BR>\n" );
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document.write( "The base used was not important to the solution because the same concepts apply regardless of the base.\r<BR>\n" );
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document.write( "If you assume n is 10, then you can solve for any m using the calculator.\r<BR>\n" );
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document.write( "If you assume n is the natural log to the base e, then you can solve for any m using the calculator.\r<BR>\n" );
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document.write( "If n is any number other than 10 or e, then you would need to use the conversion formula to solve using your calculator.\r<BR>\n" );
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document.write( "To do that, you would do the following:\r<BR>\n" );
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document.write( "Assume log of m to the base n.\r<BR>\n" );
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document.write( "Take the log of m to the base 10 and divide it by the log of n to the base 10.\r<BR>\n" );
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document.write( "You will get the same answer.\r<BR>\n" );
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document.write( "An easy example:\r<BR>\n" );
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document.write( "Log of 8 to the base 2 = 3 because 2^3 = 8.\r<BR>\n" );
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document.write( "To solve this using your calculator, you would take the log of 8 to the base 10 and divide that by the log of 2 to the base 10.\r<BR>\n" );
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document.write( "Using your calculator, you would get LOG(8) / LOG(2) = 3.\r<BR>\n" );
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document.write( "When you use your calculator, the LOG function implies the base of 10.\r<BR>\n" );
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document.write( "Similarly, when you use your calculator, the LN function implies the base of e.\r<BR>\n" );
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document.write( "You could also have done LN(8) / LN(2) and gotten the same answer of 3.\r<BR>\n" );
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document.write( "You can convert the log of any base to the log of any other base by using the conversion formula of:\r<BR>\n" );
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document.write( " </SPAN>\n" );
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