document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188010>Question 188010</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi i have a question about a Logarithm problem\r<BR>\n" );
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document.write( "log(x-6)-log(x-2)=log x/5\r<BR>\n" );
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document.write( "i understand (X-6)/(X-2) = LOG X - LOG 5\r<BR>\n" );
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document.write( "\"\"WHY DOES X GOES WITH  (X-6) AND 5 GOES WITH (X-2)\"\"\"\"\r<BR>\n" );
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document.write( "so the problem goes something like this x(x-6)/5(x-2)=10^0 =1\r<BR>\n" );
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document.write( "x^2-6x=1*5(x-2) = which is x^2-11x-10=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #140936 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=140936\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  hi i have a question about a Logarithm problem <BR>\n" );
document.write( "log(x-6)-log(x-2)=log x/5 <BR>\n" );
document.write( "i understand (X-6)/(X-2) = LOG X - LOG 5 <BR>\n" );
document.write( "\"\"WHY DOES X GOES WITH (X-6) AND 5 GOES WITH (X-2)\"\"\"\" <BR>\n" );
document.write( "so the problem goes something like this x(x-6)/5(x-2)=10^0 =1 <BR>\n" );
document.write( "x^2-6x=1*5(x-2) = which is x^2-11x-10=0<BR>\n" );
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document.write( "log(x-6)-log(x-2)=log x/5  Solve for x ?<BR>\n" );
document.write( "log((x-6)/(x-2)) = log(x/5)<BR>\n" );
document.write( "(x-6)/(x-2) = x/5<BR>\n" );
document.write( "x*(x-2) = 5*(x-6)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+2x+=+5x+-+30 ALIGN=MIDDLE  ALT=\"x%5E2+-+2x+=+5x+-+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+7x+%2B+30+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+7x+%2B+30+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-7x%2B30+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-7x%2B30+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-7%29%5E2-4%2A1%2A30=-71 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-7%29%5E2-4%2A1%2A30=-71\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The discriminant -71 is less than zero. That means that there are no solutions among real numbers.<BR><BR>\n" );
document.write( "  If you are a student of advanced school algebra and are aware about <u>imaginary numbers<u>, read on.<BR><BR>\n" );
document.write( "  <BR>\n" );
document.write( "      In the field of imaginary numbers, the square root of -71 is + or - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+71%29+=+8.42614977317636 ALIGN=MIDDLE  ALT=\"sqrt%28+71%29+=+8.42614977317636\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "  <BR>\n" );
document.write( "      The solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28--7%2B-i%2Asqrt%28+-71+%29%29%2F2%5C1+=++%28--7%2B-i%2A8.42614977317636%29%2F2%5C1+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >, or<BR>\n" );
document.write( "  Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-7%2Ax%2B30+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-7%2Ax%2B30+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "The logs of complex numbers is outside the scope of this forum.<BR>\n" );
document.write( " </SPAN>\n" );
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