document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=936216>Question 936216</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please solve : log (k+2) + log (k-1) = 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #569652 by </B><A HREF=/tutors/aboutme.mpl?userid=srinivas.g><B>srinivas.g(540)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=srinivas.g><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=srinivas.g><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=569652\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> log (k+2) + log (k-1) = 1       log 10 =1\r<BR>\n" );
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document.write( "log (k+2) + log (k-1) = log 10<BR>\n" );
document.write( " formula :  log a+log b  = log(a*b)<BR>\n" );
document.write( "   log (k+2)*(k-1)=log 10<BR>\n" );
document.write( "       (k+2)(k-1)=10<BR>\n" );
document.write( "        k(k-1)+2(k-1)=10<BR>\n" );
document.write( "           <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k%5E2%2Bk%2A%28-1%29%2B2%2Ak%2B2%2A%28-1%29++=10 ALIGN=MIDDLE  ALT=\"+k%5E2%2Bk%2A%28-1%29%2B2%2Ak%2B2%2A%28-1%29++=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "         <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k%5E2-k%2B2k-2+=10 ALIGN=MIDDLE  ALT=\"+k%5E2-k%2B2k-2+=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "        <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k%5E2%2Bk-2=10 ALIGN=MIDDLE  ALT=\"+k%5E2%2Bk-2=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "           move 10 to the left<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k%5E2%2Bk-2-10=0 ALIGN=MIDDLE  ALT=\"+k%5E2%2Bk-2-10=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "      <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k%5E2%2Bk-12=0 ALIGN=MIDDLE  ALT=\"+k%5E2%2Bk-12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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=ak%5E2%2Bbk%2Bc=0 ALIGN=MIDDLE  ALT=\"ak%5E2%2Bbk%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1k%5E2%2B1k%2B-12+=+0 ALIGN=MIDDLE  ALT=\"1k%5E2%2B1k%2B-12+=+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=k%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"k%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=%281%29%5E2-4%2A1%2A-12=49 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%281%29%5E2-4%2A1%2A-12=49\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=49 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+=+%28-1%2B-sqrt%28+49+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-1%2B-sqrt%28+49+%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=k%5B1%5D+=+%28-%281%29%2Bsqrt%28+49+%29%29%2F2%5C1+=+3 ALIGN=MIDDLE  ALT=\"k%5B1%5D+=+%28-%281%29%2Bsqrt%28+49+%29%29%2F2%5C1+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5B2%5D+=+%28-%281%29-sqrt%28+49+%29%29%2F2%5C1+=+-4 ALIGN=MIDDLE  ALT=\"k%5B2%5D+=+%28-%281%29-sqrt%28+49+%29%29%2F2%5C1+=+-4\"   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=1k%5E2%2B1k%2B-12 ALIGN=MIDDLE  ALT=\"1k%5E2%2B1k%2B-12\"   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=1k%5E2%2B1k%2B-12+=+1%28k-3%29%2A%28k--4%29 ALIGN=MIDDLE  ALT=\"1k%5E2%2B1k%2B-12+=+1%28k-3%29%2A%28k--4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 3, -4.\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%2B1%2Ax%2B-12+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-12+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "   <BR>\n" );
document.write( "   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );