document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=4212>Question 4212</A>: <I><SPAN STYLE=\"word-break: break-all;\"> simplify:-<BR>\n" );
document.write( "(log3 135)/(log15 3)  -  (log3 5)/(log405 3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #1884 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=1884\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first change the base, so that all are base 3...i will not write the base anymore, to ease the readability:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log135log15%29%2F%28log3%29+-+%28log5log405%29%2F%28log3%29 ALIGN=MIDDLE  ALT=\"%28log135log15%29%2F%28log3%29+-+%28log5log405%29%2F%28log3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since log3 to base 3 is 1, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log135log15+-+log5log405 ALIGN=MIDDLE  ALT=\"log135log15+-+log5log405\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "135 = 5*27<BR>\n" );
document.write( "405 = 5*81<BR>\n" );
document.write( "and 15 = 5*3, so we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2827%2A5%29log%283%2A5%29+-+log5log%2881%2A5%29 ALIGN=MIDDLE  ALT=\"log%2827%2A5%29log%283%2A5%29+-+log5log%2881%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(log27+log5)(log3+log5) - log5(log81+log5)\r<BR>\n" );
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document.write( "log27log3 + log27log5 + log3log5 + (log5)^2 - log81log5 - (log5)^2\r<BR>\n" );
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document.write( "Now, log27 to base 3 is 3<BR>\n" );
document.write( "and log81 to base 3 is 4, so...\r<BR>\n" );
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document.write( "3log3 + 3log5 + log5 + (log5)^2 - 4log5 - (log5)^2\r<BR>\n" );
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document.write( "everything cancels except for the 3, so this is the answer!\r<BR>\n" );
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document.write( "jon<BR>\n" );
document.write( " </SPAN>\n" );
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