document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=38201>Question 38201</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) Express loga X2 + 2 loga Square root of X as a single logarithm. Simplify if possible.\r<BR>\n" );
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document.write( "2) Given logb 2=0.387 and logb 5=0.898 find log square root of 20\r<BR>\n" );
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document.write( "3) solve   2x+3 <BR>\n" );
document.write( "         5      =125\r<BR>\n" );
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document.write( "4)logx +log(x-2)=1        <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 #23659 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=23659\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) Express loga X^2 + 2 loga Square root of X as a single logarithm. Simplify if possible. <BR>\n" );
document.write( "=2logX + 2log a = 2log(Xa)\r<BR>\n" );
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document.write( "2) Given logb 2=0.387 and logb 5=0.898 find log square root of 20 <BR>\n" );
document.write( "log20 = log(4*5) = 2log2 + log5 = 2(0.387)+0.898=1.672<BR>\n" );
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document.write( "3) solve 2x+35 =125<BR>\n" );
document.write( "2x=90<BR>\n" );
document.write( "x=45\r<BR>\n" );
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document.write( "4)logx +log(x-2)=1 <BR>\n" );
document.write( "log[x(x-2)]=1<BR>\n" );
document.write( "log[x^2-2x]=1<BR>\n" );
document.write( "x^2-2x=10<BR>\n" );
document.write( "x^2-2x-10=0<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-2x%2B-10+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-2x%2B-10+=+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=%28-2%29%5E2-4%2A1%2A-10=44 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-2%29%5E2-4%2A1%2A-10=44\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=44 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+44+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--2%2B-sqrt%28+44+%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-%28-2%29%2Bsqrt%28+44+%29%29%2F2%5C1+=+4.3166247903554 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+44+%29%29%2F2%5C1+=+4.3166247903554\"   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-%28-2%29-sqrt%28+44+%29%29%2F2%5C1+=+-2.3166247903554 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-2%29-sqrt%28+44+%29%29%2F2%5C1+=+-2.3166247903554\"   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-2x%2B-10 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-2x%2B-10\"   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-2x%2B-10+=+1%28x-4.3166247903554%29%2A%28x--2.3166247903554%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-2x%2B-10+=+1%28x-4.3166247903554%29%2A%28x--2.3166247903554%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 4.3166247903554, -2.3166247903554.\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-2%2Ax%2B-10+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-10+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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