document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149549>Question 149549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve the following...<BR>\n" );
document.write( "log6(6 is lower than the g) (x+3) + log6(6 is lower to the g)(x+4)=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109730 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=109730\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C%28x%2B3%29%29+%2B+log%286%2C%28x%2B4%29%29=1 ALIGN=MIDDLE  ALT=\"log%286%2C%28x%2B3%29%29+%2B+log%286%2C%28x%2B4%29%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C%28%28x%2B3%29%28x%2B4%29%29%29=1 ALIGN=MIDDLE  ALT=\"log%286%2C%28%28x%2B3%29%28x%2B4%29%29%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the logs on the left side using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29=log%28b%2C%28A%2AB%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29=log%28b%2C%28A%2AB%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%286%2C%28x%5E2%2B7x%2B12%29%29=1 ALIGN=MIDDLE  ALT=\"log%286%2C%28x%5E2%2B7x%2B12%29%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%5E1=x%5E2%2B7x%2B12 ALIGN=MIDDLE  ALT=\"6%5E1=x%5E2%2B7x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the equation using the property: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%29%29=y ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%29%29=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > ====> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5Ey=x ALIGN=MIDDLE  ALT=\"b%5Ey=x\"   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=6=x%5E2%2B7x%2B12 ALIGN=MIDDLE  ALT=\"6=x%5E2%2B7x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2%2B7x%2B12-6 ALIGN=MIDDLE  ALT=\"0=x%5E2%2B7x%2B12-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 6 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2%2B7x%2B6 ALIGN=MIDDLE  ALT=\"0=x%5E2%2B7x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%287%29+%2B-+sqrt%28+%287%29%5E2-4%281%29%286%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%287%29+%2B-+sqrt%28+%287%29%5E2-4%281%29%286%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=7 ALIGN=MIDDLE  ALT=\"b=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=6 ALIGN=MIDDLE  ALT=\"c=6\"   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=x+=+%28-7+%2B-+sqrt%28+49-4%281%29%286%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+sqrt%28+49-4%281%29%286%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49 ALIGN=MIDDLE  ALT=\"49\"   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=x+=+%28-7+%2B-+sqrt%28+49-24+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+sqrt%28+49-24+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%281%29%286%29 ALIGN=MIDDLE  ALT=\"4%281%29%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24 ALIGN=MIDDLE  ALT=\"24\"   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=x+=+%28-7+%2B-+sqrt%28+25+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+sqrt%28+25+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24 ALIGN=MIDDLE  ALT=\"24\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49 ALIGN=MIDDLE  ALT=\"49\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   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=x+=+%28-7+%2B-+sqrt%28+25+%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+sqrt%28+25+%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   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=x+=+%28-7+%2B-+5%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+5%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   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=x+=+%28-7+%2B+5%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B+5%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-7+-+5%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+-+5%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-2%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=++%28-12%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=++%28-12%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1 ALIGN=MIDDLE  ALT=\"x+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-6 ALIGN=MIDDLE  ALT=\"x+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "Since we cannot take the log of a negative number, this means that we must disregard the solution <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-6 ALIGN=MIDDLE  ALT=\"x+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C%28-6%2B3%29%29=log%286%2C%28-3%29%29 ALIGN=MIDDLE  ALT=\"log%286%2C%28-6%2B3%29%29=log%286%2C%28-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1 ALIGN=MIDDLE  ALT=\"x+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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