document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1037153>Question 1037153</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the Solution set of the equation e^5x+4e^3x+4e^2x=-9-3e^x+5e^4x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #651880 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=651880\">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=e%5E%285x%29%2B4e%5E%283x%29%2B4e%5E%282x%29=-9-3e%5Ex%2B5e%5E%284x%29 ALIGN=MIDDLE  ALT=\"e%5E%285x%29%2B4e%5E%283x%29%2B4e%5E%282x%29=-9-3e%5Ex%2B5e%5E%284x%29\"   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=e%5E%285x%29+-+5e%5E%284x%29+%2B4e%5E%283x%29%2B4e%5E%282x%29+%2B+3e%5Ex+%2B9+=+0 ALIGN=MIDDLE  ALT=\"e%5E%285x%29+-+5e%5E%284x%29+%2B4e%5E%283x%29%2B4e%5E%282x%29+%2B+3e%5Ex+%2B9+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+e%5Ex ALIGN=MIDDLE  ALT=\"w+=+e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Then the last equation is equivalent to \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E5+-+5w%5E4+%2B4w%5E3%2B4w%5E2+%2B+3w+%2B9+=+0 ALIGN=MIDDLE  ALT=\"w%5E5+-+5w%5E4+%2B4w%5E3%2B4w%5E2+%2B+3w+%2B9+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "By using the rational root theorem and trying out root candidates by synthetic division, you will find that --\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E5+-+5w%5E4+%2B4w%5E3%2B4w%5E2+%2B+3w+%2B9+=+%28w%2B1%29%28w-3%29%5E2%28w%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"w%5E5+-+5w%5E4+%2B4w%5E3%2B4w%5E2+%2B+3w+%2B9+=+%28w%2B1%29%28w-3%29%5E2%28w%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "==> the zeros are w = -1, 3 (double), i, -i.\r<BR>\n" );
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document.write( "Therefore the solution set of the original equation is { ln(-1), ln3, ln3, lni, ln(-i)}<BR>\n" );
document.write( "If we are after REAL zeros only, then the solution to the original equation is x = ln3, which is a double root.  ( ln(-1), lni, and ln(-i) all have values in the complex domain.)<BR>\n" );
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