document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=63903>Question 63903</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for x: e^2x + 4e^-2x = 4.\r<BR>\n" );
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document.write( "a. (1/2) ln 2<BR>\n" );
document.write( "b. (1/3) ln 2<BR>\n" );
document.write( "c. (1/3) ln 3<BR>\n" );
document.write( "d. (1/2) ln 3<BR>\n" );
document.write( "e. ln 2<BR>\n" );
document.write( "f. ln 3<BR>\n" );
document.write( "g. none of these </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #44544 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=44544\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> e^2x + 4e^-2x = 4<BR>\n" );
document.write( "Multiply thru by e^(2x) to get:<BR>\n" );
document.write( "e^4x + 4 = 4e^2x<BR>\n" );
document.write( "Rewrite as:<BR>\n" );
document.write( "(e^2x)^2-4(e^2x)+4=0<BR>\n" );
document.write( "This is a quadratic with variable e^2x.<BR>\n" );
document.write( "Let e^2x=w, then rewrite the equation as:<BR>\n" );
document.write( "w^2-4w+4=0<BR>\n" );
document.write( "(w-2)^2=0<BR>\n" );
document.write( "w=2<BR>\n" );
document.write( "Therefore e^2x=2<BR>\n" );
document.write( "Take the natural law of both sides to get:<BR>\n" );
document.write( "2x=ln2<BR>\n" );
document.write( "x=(1/2)ln2<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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