document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=668792>Question 668792</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the natural logarithmic equation algebraically. Approximate the result to three decimal places. <BR>\n" );
document.write( "1.) ln x + ln ( x + 3 ) = 1 <BR>\n" );
document.write( "2.) ln ( x + 1 ) - ln ( x - 2 ) = ln x^2 \r<BR>\n" );
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document.write( "Please help me! I need it by today I have been trying I don't get it:(  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #415850 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=415850\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do #1 to get you started.\r<BR>\n" );
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document.write( "ln( x ) + ln ( x + 3 ) = 1\r<BR>\n" );
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document.write( "ln( x(x + 3) ) = 1\r<BR>\n" );
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document.write( "x(x + 3) = e^1\r<BR>\n" );
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document.write( "x(x + 3) = e\r<BR>\n" );
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document.write( "x^2 + 3x = e\r<BR>\n" );
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document.write( "x^2 + 3x - e = 0\r<BR>\n" );
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document.write( "x^2 + 3x - 2.71828 = 0   (note: e is roughly 2.71828...)\r<BR>\n" );
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document.write( "Now use the quadratic formula to solve for x. In this case, a = 1, b = 3, and c = 2.71828\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%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=x+=+%28-%283%29%2B-sqrt%28%283%29%5E2-4%281%29%28-2.71828%29%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%283%29%2B-sqrt%28%283%29%5E2-4%281%29%28-2.71828%29%29%29%2F%282%281%29%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=x+=+%28-3%2B-sqrt%289-%28-10.87312%29%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-3%2B-sqrt%289-%28-10.87312%29%29%29%2F%282%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=x+=+%28-3%2B-sqrt%289%2B10.87312%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-3%2B-sqrt%289%2B10.87312%29%29%2F%282%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=x+=+%28-3%2B-sqrt%2819.87312%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%28-3%2B-sqrt%2819.87312%29%29%2F2\"   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=x+=+%28-3%2Bsqrt%2819.87312%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%28-3%2Bsqrt%2819.87312%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3-sqrt%2819.87312%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%28-3-sqrt%2819.87312%29%29%2F2\"   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=x+=+%28-3%2B4.4579278%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%28-3%2B4.4579278%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3-4.4579278%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%28-3-4.4579278%29%2F2\"   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=x+=+0.7289639 ALIGN=MIDDLE  ALT=\"x+=+0.7289639\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3.7289639 ALIGN=MIDDLE  ALT=\"x+=+-3.7289639\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the possible answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0.7289639 ALIGN=MIDDLE  ALT=\"x+=+0.7289639\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3.7289639 ALIGN=MIDDLE  ALT=\"x+=+-3.7289639\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "However, plugging in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3.7289639 ALIGN=MIDDLE  ALT=\"x+=+-3.7289639\"   DISABLED_style= \"max-width:90%; height:auto;\" > yields a negative argument in the log, which is not allowed. So we must toss out this x value.\r<BR>\n" );
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document.write( "So the only solution (to 3 decimal places) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0.729 ALIGN=MIDDLE  ALT=\"x+=+0.729\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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