document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=453069>Question 453069</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the positive root of the following equation: <BR>\n" );
document.write( "log3(c - 4) + log3(c + 6) = 4. \r<BR>\n" );
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document.write( "(Please round your answer to one decimal place.)<BR>\n" );
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document.write( " Answer   <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #311307 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=311307\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> log3(c - 4) + log3(c + 6) = 4<BR>\n" );
document.write( "log3(c - 4)(c + 6) = 4<BR>\n" );
document.write( "(c - 4)(c + 6) = 3^4<BR>\n" );
document.write( "c^2 + 6c - 4c -24 = 81<BR>\n" );
document.write( "c^2 + 2c -105 = 0<BR>\n" );
document.write( "apply the quadratic formula to find the roots:<BR>\n" );
document.write( "c = {9.3, -11.3}<BR>\n" );
document.write( "throw out the negative root leaving:<BR>\n" );
document.write( "c = 9.3<BR>\n" );
document.write( ".<BR>\n" );
document.write( "details of quadratic to follow:<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=ac%5E2%2Bbc%2Bc=0 ALIGN=MIDDLE  ALT=\"ac%5E2%2Bbc%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1c%5E2%2B2c%2B-105+=+0 ALIGN=MIDDLE  ALT=\"1c%5E2%2B2c%2B-105+=+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=c%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"c%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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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=%282%29%5E2-4%2A1%2A-105=424 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%282%29%5E2-4%2A1%2A-105=424\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=424 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+=+%28-2%2B-sqrt%28+424+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-2%2B-sqrt%28+424+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5B1%5D+=+%28-%282%29%2Bsqrt%28+424+%29%29%2F2%5C1+=+9.295630140987 ALIGN=MIDDLE  ALT=\"c%5B1%5D+=+%28-%282%29%2Bsqrt%28+424+%29%29%2F2%5C1+=+9.295630140987\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5B2%5D+=+%28-%282%29-sqrt%28+424+%29%29%2F2%5C1+=+-11.295630140987 ALIGN=MIDDLE  ALT=\"c%5B2%5D+=+%28-%282%29-sqrt%28+424+%29%29%2F2%5C1+=+-11.295630140987\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1c%5E2%2B2c%2B-105 ALIGN=MIDDLE  ALT=\"1c%5E2%2B2c%2B-105\"   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=1c%5E2%2B2c%2B-105+=+1%28c-9.295630140987%29%2A%28c--11.295630140987%29 ALIGN=MIDDLE  ALT=\"1c%5E2%2B2c%2B-105+=+1%28c-9.295630140987%29%2A%28c--11.295630140987%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 9.295630140987, -11.295630140987.\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%2B2%2Ax%2B-105+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-105+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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