document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=691401>Question 691401</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2log%289%2Cx%29+=+1%2F2+%2B+log%289%2C%285x+%2B+18%29%29+ ALIGN=MIDDLE  ALT=\"+2log%289%2Cx%29+=+1%2F2+%2B+log%289%2C%285x+%2B+18%29%29+\"   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 #426672 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=426672\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2log(base9)x = 1/2 + log(base9)(5x + 18)<BR>\n" );
document.write( "log(base9)x^2 = 1/2 + log(base9)(5x + 18)<BR>\n" );
document.write( "log(base9)x^2 - log(base9)(5x + 18) = 1/2<BR>\n" );
document.write( "log(base9)x^2/(5x + 18) = 1/2<BR>\n" );
document.write( "x^2/(5x + 18) = 9^(1/2)<BR>\n" );
document.write( "x^2/(5x + 18) = 3<BR>\n" );
document.write( "x^2 = 3(5x + 18)<BR>\n" );
document.write( "x^2 = 15x + 46<BR>\n" );
document.write( "x^2-15X = 46<BR>\n" );
document.write( "x^2-15X-46 = 0<BR>\n" );
document.write( "Applying the \"quadratic formula\" yields:<BR>\n" );
document.write( "x  = {17.61, -2.61}<BR>\n" );
document.write( "throw out the negative solution (extraneous) leaving:<BR>\n" );
document.write( "x = 17.61<BR>\n" );
document.write( ".<BR>\n" );
document.write( "details of quadratic follows:<BR>\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-15x%2B-46+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-15x%2B-46+=+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=%28-15%29%5E2-4%2A1%2A-46=409 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-15%29%5E2-4%2A1%2A-46=409\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=409 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--15%2B-sqrt%28+409+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--15%2B-sqrt%28+409+%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-%28-15%29%2Bsqrt%28+409+%29%29%2F2%5C1+=+17.6118742080783 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-15%29%2Bsqrt%28+409+%29%29%2F2%5C1+=+17.6118742080783\"   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-%28-15%29-sqrt%28+409+%29%29%2F2%5C1+=+-2.61187420807834 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-15%29-sqrt%28+409+%29%29%2F2%5C1+=+-2.61187420807834\"   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-15x%2B-46 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-15x%2B-46\"   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-15x%2B-46+=+1%28x-17.6118742080783%29%2A%28x--2.61187420807834%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-15x%2B-46+=+1%28x-17.6118742080783%29%2A%28x--2.61187420807834%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 17.6118742080783, -2.61187420807834.\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-15%2Ax%2B-46+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-15%2Ax%2B-46+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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