document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=507911>Question 507911</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation e^ { 2 x } - 11 e^ { x } +30 = 0 has two solutions. \r<BR>\n" );
document.write( "\n" );
document.write( "The smaller one is:<BR>\n" );
document.write( "and the larger one is:  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #341055 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=341055\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation e^ { 2 x } - 11 e^ { x } +30 = 0 has two solutions. <BR>\n" );
document.write( "The smaller one is:<BR>\n" );
document.write( "and the larger one is:<BR>\n" );
document.write( "**<BR>\n" );
document.write( "e^ { 2 x } - 11 e^ { x } +30 = 0<BR>\n" );
document.write( "e^2x-11^x+30=0<BR>\n" );
document.write( "let u=e^x<BR>\n" );
document.write( "u^2=e^2x<BR>\n" );
document.write( "u^2-11u+30=0<BR>\n" );
document.write( "(u-6)(u-5)=0<BR>\n" );
document.write( "u=6<BR>\n" );
document.write( "or <BR>\n" );
document.write( "u=5<BR>\n" );
document.write( "...<BR>\n" );
document.write( "for u=6<BR>\n" );
document.write( "e^x=6<BR>\n" );
document.write( "take ln of both sides<BR>\n" );
document.write( "lne^x=ln6<BR>\n" );
document.write( "x=1.7918<BR>\n" );
document.write( "..<BR>\n" );
document.write( "for u=5<BR>\n" );
document.write( "e^x=5<BR>\n" );
document.write( "take ln of both sides<BR>\n" );
document.write( "lne^x=ln5<BR>\n" );
document.write( "x=1.6094<BR>\n" );
document.write( "..<BR>\n" );
document.write( "ans:<BR>\n" );
document.write( "x=1.7918<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x=1.6094 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );