document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1028184>Question 1028184</A>: <I><SPAN STYLE=\"word-break: break-all;\"> We were asked to solve logarithmic inequations, and although I could solve it, I stopped at a dead end, in which I couldn't find a ''good'' answer.. <BR>\n" );
document.write( "i) 2*ln(x+2)-1 > 0 <BR>\n" );
document.write( "ii) log(3-2x) > 1 + log(x+5)\r<BR>\n" );
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document.write( "*Sorry if I posted this again* </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #643329 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=643329\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ln%28x%2B2%29-1+%3E+0+ ALIGN=MIDDLE  ALT=\"2ln%28x%2B2%29-1+%3E+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%2B2%29+%3E+1%2F2 ALIGN=MIDDLE  ALT=\"ln%28x%2B2%29+%3E+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2+%3E+e%5E%281%2F2%29+=+sqrt%28e%29 ALIGN=MIDDLE  ALT=\"x%2B2+%3E+e%5E%281%2F2%29+=+sqrt%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E+sqrt%28e%29+-+2 ALIGN=MIDDLE  ALT=\"x+%3E+sqrt%28e%29+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#x2248 -0.35.\r<BR>\n" );
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document.write( "ii)  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%283-2x%29%29+%3E+1+%2B+log%28%28x%2B5%29%29+ ALIGN=MIDDLE  ALT=\"log%28%283-2x%29%29+%3E+1+%2B+log%28%28x%2B5%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%283-2x%29%2F%28x%2B5%29%29+%3E+1 ALIGN=MIDDLE  ALT=\"log%28%283-2x%29%2F%28x%2B5%29%29+%3E+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-2x%29%2F%28x%2B5%29+%3E+10 ALIGN=MIDDLE  ALT=\"%283-2x%29%2F%28x%2B5%29+%3E+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-2x%29%2F%28x%2B5%29+-+10+%3E0 ALIGN=MIDDLE  ALT=\"%283-2x%29%2F%28x%2B5%29+-+10+%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-2x-10x-50%29%2F%28x%2B5%29%3E0 ALIGN=MIDDLE  ALT=\"%283-2x-10x-50%29%2F%28x%2B5%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-12x+-+47%29%2F%28x%2B5%29+%3E+0 ALIGN=MIDDLE  ALT=\"%28-12x+-+47%29%2F%28x%2B5%29+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The critical numbers are -47/12 and -5.  (The numbers that make the numerator and denominator equal to zero.)<BR>\n" );
document.write( "Choose test numbers -6, -4, and 0.  (Corresponding to the partition (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >,-5), (-5,-47/12), (-47/12, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >). )<BR>\n" );
document.write( "Upon substitution into  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-12x+-+47%29%2F%28x%2B5%29 ALIGN=MIDDLE  ALT=\"%28-12x+-+47%29%2F%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the signs are (-), (+), and (-).<BR>\n" );
document.write( "Therefore the solution is the open interval (-5,-47/12).  </SPAN>\n" );
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