document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=246678>Question 246678</A>: <I><SPAN STYLE=\"word-break: break-all;\"> log[3](1-x)+log[3](2-x)=log[3](7)  the numbers in brackets are the bases. Please help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #180053 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=180053\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> log[3](1-x)+log[3](2-x)=log[3](7)<BR>\n" );
document.write( "log[3](1-x)(2-x)=log[3](7)<BR>\n" );
document.write( "(1-x)(2-x)=7<BR>\n" );
document.write( "2-x-2x+x^2=7<BR>\n" );
document.write( "2-3x+x^2=7<BR>\n" );
document.write( "x^2-3x+2=7<BR>\n" );
document.write( "x^2-3x-5=0<BR>\n" );
document.write( "Applying the quadratic equation will yield:<BR>\n" );
document.write( "x = {4.193, -1.193}<BR>\n" );
document.write( "Checking for extraneous solutions:<BR>\n" );
document.write( "We can throw out the 4.193 solution because it will give us a negative log. So:<BR>\n" );
document.write( "x = {-1.193}<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Details of quadratic to follow:<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=quadratic.solver>SOLVE quadratic equation with variable</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-3x%2B-5+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-3x%2B-5+=+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=%28-3%29%5E2-4%2A1%2A-5=29 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-3%29%5E2-4%2A1%2A-5=29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=29 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--3%2B-sqrt%28+29+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--3%2B-sqrt%28+29+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+29+%29%29%2F2%5C1+=+4.19258240356725 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+29+%29%29%2F2%5C1+=+4.19258240356725\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-3%29-sqrt%28+29+%29%29%2F2%5C1+=+-1.19258240356725 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-3%29-sqrt%28+29+%29%29%2F2%5C1+=+-1.19258240356725\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-3x%2B-5 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-3x%2B-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-3x%2B-5+=+1%28x-4.19258240356725%29%2A%28x--1.19258240356725%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-3x%2B-5+=+1%28x-4.19258240356725%29%2A%28x--1.19258240356725%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 4.19258240356725, -1.19258240356725.\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-3%2Ax%2B-5+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-3%2Ax%2B-5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );