document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171046>Question 171046</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you condense a problem like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log3-log4-log7+ ALIGN=MIDDLE  ALT=\"+log3-log4-log7+\"   DISABLED_style= \"max-width:90%; height:auto;\" >? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126268 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=126268\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "The appropriate logarithm rules to apply are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2Cx%5B1%5D%29%2Blog%28b%2Cx%5B2%5D%29=log%28b%2C%28x%5B1%5D%2Ax%5B2%5D%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2Cx%5B1%5D%29%2Blog%28b%2Cx%5B2%5D%29=log%28b%2C%28x%5B1%5D%2Ax%5B2%5D%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2Cx%5B1%5D%29-log%28b%2Cx%5B2%5D%29=log%28b%2C%28x%5B1%5D%2Fx%5B2%5D%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2Cx%5B1%5D%29-log%28b%2Cx%5B2%5D%29=log%28b%2C%28x%5B1%5D%2Fx%5B2%5D%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "First thing is to apply the Associative and Distributive Properties:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%29-log%284%29-log%287%29=log%283%29-%28log%284%29%2Blog%287%29%29 ALIGN=MIDDLE  ALT=\"log%283%29-log%284%29-log%287%29=log%283%29-%28log%284%29%2Blog%287%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now, using Rule 1., you can render the part in parentheses as:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2828%29 ALIGN=MIDDLE  ALT=\"log%2828%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and substitute, thus:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%29-log%2828%29 ALIGN=MIDDLE  ALT=\"log%283%29-log%2828%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now apply rule 2., thus:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2F28%29 ALIGN=MIDDLE  ALT=\"log%283%2F28%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F28 ALIGN=MIDDLE  ALT=\"3%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" > is already reduced to lowest terms, you are done.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Check the reasonability of your answer with a calculator:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%29+=+0.4771 ALIGN=MIDDLE  ALT=\"log%283%29+=+0.4771\"   DISABLED_style= \"max-width:90%; height:auto;\" > (roughly)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%29+=+0.6021 ALIGN=MIDDLE  ALT=\"log%284%29+=+0.6021\"   DISABLED_style= \"max-width:90%; height:auto;\" > (roughly)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%287%29+=+0.8451 ALIGN=MIDDLE  ALT=\"log%287%29+=+0.8451\"   DISABLED_style= \"max-width:90%; height:auto;\" > (roughly)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.4771+-+0.6021+=+-0.125 ALIGN=MIDDLE  ALT=\"0.4771+-+0.6021+=+-0.125\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.125+-+0.8451+=+-0.9701 ALIGN=MIDDLE  ALT=\"-0.125+-+0.8451+=+-0.9701\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So far, so good.  Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C1%29=0 ALIGN=MIDDLE  ALT=\"log%2810%2C1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the log of something smaller than 1, in particular <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F28 ALIGN=MIDDLE  ALT=\"3%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be less than zero.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Again, from the calculator:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F28+=+0.1071 ALIGN=MIDDLE  ALT=\"3%2F28+=+0.1071\"   DISABLED_style= \"max-width:90%; height:auto;\" > (roughly) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%280.1071%29+=+-0.9072 ALIGN=MIDDLE  ALT=\"log%280.1071%29+=+-0.9072\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Close enough. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );