document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=449498>Question 449498</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find x,\r<BR>\n" );
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document.write( "Log{base x}5=8+Log{base 9}x\r<BR>\n" );
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document.write( "for the left x is the base. for right 9 is the base. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #309226 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=309226\">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%28x%2C5%29+=+8+%2B+log%289%2Cx%29 ALIGN=MIDDLE  ALT=\"log%28x%2C5%29+=+8+%2B+log%289%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "log(5)/log(x) = 8 + log(x)/log(9) = [8*log(9) + log(x)]/log(9)<BR>\n" );
document.write( "log(5)/log(x) = (8*log(9) + log(x))/log(9)<BR>\n" );
document.write( "log(5)*log(9) = log(x)*(8log(9) + log(x))<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log%28x%29%29%5E2+%2B+8%2Alog%289%29%2Alog%28x%29+-+log%285%29log%289%29+=+0 ALIGN=MIDDLE  ALT=\"%28log%28x%29%29%5E2+%2B+8%2Alog%289%29%2Alog%28x%29+-+log%285%29log%289%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sub u for log(x)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E2+%2B+8%2Alog%289%29%2Au+-+log%285%29%2Alog%289%29+=+0 ALIGN=MIDDLE  ALT=\"u%5E2+%2B+8%2Alog%289%29%2Au+-+log%285%29%2Alog%289%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E2+%2B+7.63394u+-+0.6669869+=+0 ALIGN=MIDDLE  ALT=\"u%5E2+%2B+7.63394u+-+0.6669869+=+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%2B76.3394x%2B0.6669869+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B76.3394x%2B0.6669869+=+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=%2876.3394%29%5E2-4%2A1%2A0.6669869=5825.03604476 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2876.3394%29%5E2-4%2A1%2A0.6669869=5825.03604476\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=5825.03604476 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+=+%28-76.3394%2B-sqrt%28+5825.03604476+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-76.3394%2B-sqrt%28+5825.03604476+%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-%2876.3394%29%2Bsqrt%28+5825.03604476+%29%29%2F2%5C1+=+-0.00873812546124952 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2876.3394%29%2Bsqrt%28+5825.03604476+%29%29%2F2%5C1+=+-0.00873812546124952\"   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-%2876.3394%29-sqrt%28+5825.03604476+%29%29%2F2%5C1+=+-76.3306618745387 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2876.3394%29-sqrt%28+5825.03604476+%29%29%2F2%5C1+=+-76.3306618745387\"   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%2B76.3394x%2B0.6669869 ALIGN=MIDDLE  ALT=\"1x%5E2%2B76.3394x%2B0.6669869\"   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%2B76.3394x%2B0.6669869+=+%28x--0.00873812546124952%29%2A%28x--76.3306618745387%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B76.3394x%2B0.6669869+=+%28x--0.00873812546124952%29%2A%28x--76.3306618745387%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.00873812546124952, -76.3306618745387.\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%2B76.3394%2Ax%2B0.6669869+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B76.3394%2Ax%2B0.6669869+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "x1 and x2 are the logs of x.<BR>\n" );
document.write( "x = 0.980080785<BR>\n" );
document.write( "x = 4.670228502E-77<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );