document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042383>Question 1042383</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I express this as a single logarithm?\r<BR>\n" );
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document.write( "log5+ 2log2+log3-log6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #657342 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=657342\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm assuming these logs are all base 10.\r<BR>\n" );
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document.write( "We'll use the following rules:\r<BR>\n" );
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document.write( "Rule 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28x%29%29%2Blog%28%28y%29%29+=+log%28%28x%2Ay%29%29 ALIGN=MIDDLE  ALT=\"log%28%28x%29%29%2Blog%28%28y%29%29+=+log%28%28x%2Ay%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Rule 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28x%29%29-log%28%28y%29%29+=+log%28%28x%2Fy%29%29 ALIGN=MIDDLE  ALT=\"log%28%28x%29%29-log%28%28y%29%29+=+log%28%28x%2Fy%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Rule 3: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Alog%28%28x%29%29+=+log%28%28x%5Ey%29%29 ALIGN=MIDDLE  ALT=\"y%2Alog%28%28x%29%29+=+log%28%28x%5Ey%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Rule 4: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28b%29%29+=+1 ALIGN=MIDDLE  ALT=\"log%28b%2C%28b%29%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > where b is not equal to 1 and b > 0. In this case, I'm assuming the value of b is 10. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%285%29%29%2B2%2Alog%28%282%29%29%2Blog%28%283%29%29-log%28%286%29%29 ALIGN=MIDDLE  ALT=\"log%28%285%29%29%2B2%2Alog%28%282%29%29%2Blog%28%283%29%29-log%28%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%285%29%29%2Blog%28%282%5E2%29%29%2Blog%28%283%29%29-log%28%286%29%29 ALIGN=MIDDLE  ALT=\"log%28%285%29%29%2Blog%28%282%5E2%29%29%2Blog%28%283%29%29-log%28%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use Rule 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%285%29%29%2Blog%28%284%29%29%2Blog%28%283%29%29-log%28%286%29%29 ALIGN=MIDDLE  ALT=\"log%28%285%29%29%2Blog%28%284%29%29%2Blog%28%283%29%29-log%28%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%285%2A4%29%29%2Blog%28%283%29%29-log%28%286%29%29 ALIGN=MIDDLE  ALT=\"log%28%285%2A4%29%29%2Blog%28%283%29%29-log%28%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use Rule 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%2820%29%29%2Blog%28%283%29%29-log%28%286%29%29 ALIGN=MIDDLE  ALT=\"log%28%2820%29%29%2Blog%28%283%29%29-log%28%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%2820%2A3%29%29-log%28%286%29%29 ALIGN=MIDDLE  ALT=\"log%28%2820%2A3%29%29-log%28%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use Rule 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%2860%29%29-log%28%286%29%29 ALIGN=MIDDLE  ALT=\"log%28%2860%29%29-log%28%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28%2860%29%2F%286%29%29%29 ALIGN=MIDDLE  ALT=\"log%28%28%2860%29%2F%286%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use Rule 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%2810%29%29 ALIGN=MIDDLE  ALT=\"log%28%2810%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use Rule 4\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%285%29%29%2B2%2Alog%28%282%29%29%2Blog%28%283%29%29-log%28%286%29%29 ALIGN=MIDDLE  ALT=\"log%28%285%29%29%2B2%2Alog%28%282%29%29%2Blog%28%283%29%29-log%28%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%285%29%29%2B2%2Alog%28%282%29%29%2Blog%28%283%29%29-log%28%286%29%29=1 ALIGN=MIDDLE  ALT=\"log%28%285%29%29%2B2%2Alog%28%282%29%29%2Blog%28%283%29%29-log%28%286%29%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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