document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=209731>Question 209731</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i worked this problem like this:<BR>\n" );
document.write( "e^2x - 3e^x + 2 = 0<BR>\n" );
document.write( "e^2x - 3e^x = -2<BR>\n" );
document.write( "e^(2x\x^3) = e^(-2)<BR>\n" );
document.write( "(2\x^2)= e^(-2)<BR>\n" );
document.write( "2= e^(-2x^2)<BR>\n" );
document.write( "(2\e^-2) = x^2<BR>\n" );
document.write( "sqrt(14.778)= sqrt(x^2)<BR>\n" );
document.write( "x=3.844\r<BR>\n" );
document.write( "\n" );
document.write( "i tried my answer. but it doesnt work out.<BR>\n" );
document.write( "what did i do wrong?<BR>\n" );
document.write( "thanks  in advance<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #158587 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=158587\">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%282x%29+-+3e%5Ex+%2B+2+=+0 ALIGN=MIDDLE  ALT=\"e%5E%282x%29+-+3e%5Ex+%2B+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%282x%29+-+3e%5Ex+=+-2 ALIGN=MIDDLE  ALT=\"e%5E%282x%29+-+3e%5Ex+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Not wrong, but doesn't help.<BR>\n" );
document.write( "e^((2x)/(x^3)) = e^(-2)<BR>\n" );
document.write( "???! There is no way to arrive at this statement from the previous one.<br><BR>\n" );
document.write( "The key to solving the equation, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%282x%29+-+3e%5Ex+%2B+2+=+0 ALIGN=MIDDLE  ALT=\"e%5E%282x%29+-+3e%5Ex+%2B+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, is to recognize that<ul><li><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%282x%29+=+%28e%5Ex%29%5E2 ALIGN=MIDDLE  ALT=\"e%5E%282x%29+=+%28e%5Ex%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li><li>the equation can then be written as: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28e%5Ex%29%5E2+-+3e%5Ex+%2B+2+=+0 ALIGN=MIDDLE  ALT=\"%28e%5Ex%29%5E2+-+3e%5Ex+%2B+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li><li>the equation is therefore a quadratic equation in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex ALIGN=MIDDLE  ALT=\"e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li></ul><BR>\n" );
document.write( "If you have trouble seeing the last two, we can use a substitution to make it clearer. Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+=+e%5Ex ALIGN=MIDDLE  ALT=\"q+=+e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Replacing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex ALIGN=MIDDLE  ALT=\"e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > with q we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%5E2+-+3q+%2B+2+=+0 ALIGN=MIDDLE  ALT=\"q%5E2+-+3q+%2B+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "We can solve this for q (aka <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex ALIGN=MIDDLE  ALT=\"e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >) with the quadratic formula or by factoring:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28q+-+2%29%28q+-+1%29+=+0 ALIGN=MIDDLE  ALT=\"%28q+-+2%29%28q+-+1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In order for this product to be zero, one of the factors must be zero:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+-+2+=+0 ALIGN=MIDDLE  ALT=\"q+-+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+-+1+=+0 ALIGN=MIDDLE  ALT=\"q+-+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving these we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+=+2 ALIGN=MIDDLE  ALT=\"q+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+=+1 ALIGN=MIDDLE  ALT=\"q+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Of course we are not interested in \"q\". We are interested in \"x\". So we can substitute back in for \"q\":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex+=+2 ALIGN=MIDDLE  ALT=\"e%5Ex+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex+=+1 ALIGN=MIDDLE  ALT=\"e%5Ex+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To solve these for x we will find the natural log of each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%5Ex%29+=+ln%282%29 ALIGN=MIDDLE  ALT=\"ln%28e%5Ex%29+=+ln%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%5Ex%29+=+ln%281%29 ALIGN=MIDDLE  ALT=\"ln%28e%5Ex%29+=+ln%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using one of the properties of logarithms: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C+%28x%5Ey%29%29+=+y%2Alog%28a%2C+x%29 ALIGN=MIDDLE  ALT=\"log%28a%2C+%28x%5Ey%29%29+=+y%2Alog%28a%2C+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get:<BR>\n" );
document.write( "x*ln(e) = ln(2) or x*ln(e) = ln(1)<BR>\n" );
document.write( "Since the ln(e) is 1 by definition and ln(1) is zero:<BR>\n" );
document.write( "x = ln(2) or x = 0 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );