document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=831686>Question 831686</A>: <I><SPAN STYLE=\"word-break: break-all;\"> e^x-e^-x=1 Hint: multiply e^x on both sides<BR>\n" );
document.write( "I know this involves natural log but I have no idea what to do. Please help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #501567 by </B><A HREF=/tutors/aboutme.mpl?userid=hovuquocan1997><B>hovuquocan1997(83)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=hovuquocan1997><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=501567\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have e^-x = 1/e^x (convert)<BR>\n" );
document.write( "So the equation will become<BR>\n" );
document.write( "e^x - 1/e^x = 1 <BR>\n" );
document.write( "multiply e^x like you said<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex%2Ae%5Ex+-+1+=+e%5Ex ALIGN=MIDDLE  ALT=\"e%5Ex%2Ae%5Ex+-+1+=+e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28e%5Ex%29%5E2+-+e%5Ex+-+1+=+0 ALIGN=MIDDLE  ALT=\"%28e%5Ex%29%5E2+-+e%5Ex+-+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then you can let e^x = a and the equation will become<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+-+a+-+1+=+0 ALIGN=MIDDLE  ALT=\"a%5E2+-+a+-+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can solve this equation using quadratic formula, then you will get two answer<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Bsqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"%281%2Bsqrt%285%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-sqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"%281-sqrt%285%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Remember you let e^x = a? Now change a into e^x <BR>\n" );
document.write( "You have <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;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Bsqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"%281%2Bsqrt%285%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then you use natural log on both side, you will have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28%281%2Bsqrt%285%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"ln%28%281%2Bsqrt%285%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then use calculator to find it<BR>\n" );
document.write( "And then you find another answer with <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;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-sqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"%281-sqrt%285%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > using the same method<BR>\n" );
document.write( "TA-DAH </SPAN>\n" );
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