document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=220511>Question 220511</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help me with this problem?\r<BR>\n" );
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document.write( "If e^{2x} + 4e^{x} = +12, then x = </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #165520 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=165520\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Can someone help me with this problem? <BR>\n" );
document.write( "If e^{2x} + 4e^{x} = +12, then x =<BR>\n" );
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document.write( "That is a quadratic function with variable = e^x<BR>\n" );
document.write( "Let e^x = w<BR>\n" );
document.write( "Rewrite the equation and solve for \"w\":<BR>\n" );
document.write( "w^2 + 4w - 12 = 0<BR>\n" );
document.write( "Factor:<BR>\n" );
document.write( "(w+6)(w-2) = 0<BR>\n" );
document.write( "w = -6 or w = 2<BR>\n" );
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document.write( "Substitute back to e^x<BR>\n" );
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document.write( "e^x = -6 or e^x = 2<BR>\n" );
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document.write( "Solve for \"x\":<BR>\n" );
document.write( "e^x cannot be negative so it cannot be -6.<BR>\n" );
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document.write( "e^x = 2<BR>\n" );
document.write( "x = ln2 is the only solution.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "stan H. </SPAN>\n" );
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