document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=87641>Question 87641</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a^2+b^2 = 7ab, show that log a+b/3=1/2 (loga + logb) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #63556 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=63556\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Starting with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28%28a%2Bb%29%2F3%29+=+%281%2F2%29%28loga+%2B+logb%29+ ALIGN=MIDDLE  ALT=\"+log%28%28a%2Bb%29%2F3%29+=+%281%2F2%29%28loga+%2B+logb%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > i shall re-write it as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2log%28%28a%2Bb%29%2F3%29+=+%28loga+%2B+logb%29+ ALIGN=MIDDLE  ALT=\"+2log%28%28a%2Bb%29%2F3%29+=+%28loga+%2B+logb%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "I am going to prove this is correct instead by looking at the Left hand side <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2log%28%28a%2Bb%29%2F3%29+ ALIGN=MIDDLE  ALT=\"+2log%28%28a%2Bb%29%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and showing that it equals the right hand side <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28loga+%2B+logb%29+ ALIGN=MIDDLE  ALT=\"+%28loga+%2B+logb%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2log%28%28a%2Bb%29%2F3%29+ ALIGN=MIDDLE  ALT=\"+2log%28%28a%2Bb%29%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28%28%28a%2Bb%29%2F3%29%29%5E2+ ALIGN=MIDDLE  ALT=\"+log%28%28%28a%2Bb%29%2F3%29%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> one of laws of Logs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28%28a%5E2%2B2ab%2Bb%5E2%29%2F9%29+ ALIGN=MIDDLE  ALT=\"+log%28%28a%5E2%2B2ab%2Bb%5E2%29%2F9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> multiply out brackets\r<BR>\n" );
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document.write( "now we are told that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%5E2%2Bb%5E2+=+7ab+ ALIGN=MIDDLE  ALT=\"+a%5E2%2Bb%5E2+=+7ab+\"   DISABLED_style= \"max-width:90%; height:auto;\" > so sub that into what we have and we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28%28a%5E2%2Bb%5E2%2B2ab%29%2F9%29+ ALIGN=MIDDLE  ALT=\"+log%28%28a%5E2%2Bb%5E2%2B2ab%29%2F9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > re-arrange order so you can see the squared terms together<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28%287ab%2B2ab%29%2F9%29+ ALIGN=MIDDLE  ALT=\"+log%28%287ab%2B2ab%29%2F9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> sub in the other equality<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28%289ab%29%2F9%29+ ALIGN=MIDDLE  ALT=\"+log%28%289ab%29%2F9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> add together like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28ab%29+ ALIGN=MIDDLE  ALT=\"+log%28ab%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> cancel out the 9's<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28a%29+%2B+log%28b%29+ ALIGN=MIDDLE  ALT=\"+log%28a%29+%2B+log%28b%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > use one of the Laws of Logs\r<BR>\n" );
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document.write( "which is what i set out to prove it equalled.\r<BR>\n" );
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document.write( "cheers<BR>\n" );
document.write( "jon<BR>\n" );
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