document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=34436>Question 34436</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C3x%2B6%29-log%283%2Cx-6%29=2 ALIGN=MIDDLE  ALT=\"log%283%2C3x%2B6%29-log%283%2Cx-6%29=2\"   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 #20691 by </B><A HREF=/tutors/aboutme.mpl?userid=dimndskier><B>dimndskier(8)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dimndskier><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=20691\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First you have to understand that the subtraction (to keep wording and explanation simple) of two logarithmic expressions is equal to the logarithm of them in a fraction, no matter what the base is.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%283%2Cx%5E5%29+-+log%283%2Cx%5E2%29+=+log%283%2C%28%28x%5E5%29%2F%28x%5E2%29%29%29+=+log%283%2Cx%5E3%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore if I use 9 and substitute in for x, we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%283%2C9%5E5%29+-+log%283%2C9%5E2%29+=+log%283%2C%28%289%5E5%29%2F%289%5E2%29%29%29+=+log%283%2C9%5E3%29+=+log%283%2C729%29+=+6 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Before I help with this problem, you must understand what the purpose of logarithms really are.\r<BR>\n" );
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document.write( "To put it simply, sometimes you know the BASE value of an expression (BASE), and in the same expression you don't know the power (EXPONENT) that produces the answer (ANSWER).\r<BR>\n" );
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document.write( "So, here's an easy way to remember WHY you use this mathematical function:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28BASE%2CANSWER%29=%28EXPONENT%29+ ALIGN=MIDDLE  ALT=\"+log%28BASE%2CANSWER%29=%28EXPONENT%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "How does this work?\r<BR>\n" );
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document.write( "Well, we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%5E2=9+ ALIGN=MIDDLE  ALT=\"+3%5E2=9+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%283%2C9%29+=+2+ ALIGN=MIDDLE  ALT=\"+log%283%2C9%29+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, get it?\r<BR>\n" );
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document.write( "In your problem however there is the necessity of keep tracking of the algebraic expressions as the functions of the logarithms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C3x%2B6%29-log%283%2Cx-6%29=2 ALIGN=MIDDLE  ALT=\"log%283%2C3x%2B6%29-log%283%2Cx-6%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here is how we work this problem, really...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%283%2C%283x%2B6%29%29-log%283%2C%28x-6%29%29+=+2+ ALIGN=MIDDLE  ALT=\"+log%283%2C%283x%2B6%29%29-log%283%2C%28x-6%29%29+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this can be rewritten as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%283%2C%28%283x%2B6%29%2F%28x-6%29%29%29+=+2+ ALIGN=MIDDLE  ALT=\"+log%283%2C%28%283x%2B6%29%2F%28x-6%29%29%29+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Don't forget why we use logarithm... to find the answer when we know the base and answer.\r<BR>\n" );
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document.write( "So, we have the base of 3 and exponent of 2, which means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2 ALIGN=MIDDLE  ALT=\"3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then is simplified to 9!\r<BR>\n" );
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document.write( "Now we REALLY have to solve this problem:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%283x%2B6%29%2F%28x-6%29%29+=+9+ ALIGN=MIDDLE  ALT=\"+%28%283x%2B6%29%2F%28x-6%29%29+=+9+\"   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=+%28%283x%2B6%29%2F%28x-6%29%29%2A%28x-6%29+=+9%2A%28x-6%29+ ALIGN=MIDDLE  ALT=\"+%28%283x%2B6%29%2F%28x-6%29%29%2A%28x-6%29+=+9%2A%28x-6%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=+%283x%2B6%29+=+9%2A%28x-6%29+ ALIGN=MIDDLE  ALT=\"+%283x%2B6%29+=+9%2A%28x-6%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=+3x%2B6+=+9x-54+ ALIGN=MIDDLE  ALT=\"+3x%2B6+=+9x-54+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which then becomes...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x%2B6+-+%283x%2B6%29+=+9x-54-%283x%2B6%29+ ALIGN=MIDDLE  ALT=\"+3x%2B6+-+%283x%2B6%29+=+9x-54-%283x%2B6%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=+0+=+9x+-+54+-+3x+-+6+ ALIGN=MIDDLE  ALT=\"+0+=+9x+-+54+-+3x+-+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6x-60=0+ ALIGN=MIDDLE  ALT=\"+6x-60=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and then we discover that x=10\r<BR>\n" );
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document.write( "The final answer is x=6.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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