document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170635>Question 170635</A>: <I><SPAN STYLE=\"word-break: break-all;\"> e^4X-e^2X-6=0\r<BR>\n" );
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document.write( "How do I solve for X using natural logs?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #125952 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=125952\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> e^4X-e^2X-6=0<BR>\n" );
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document.write( "Let w = e^2x<BR>\n" );
document.write( "Substitute to get:\r<BR>\n" );
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document.write( "w^2 -w - 6 = 0<BR>\n" );
document.write( "(w-3)(w+2) = 0<BR>\n" );
document.write( "w = 3 or w = -2<BR>\n" );
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document.write( "Solve for \"x\":<BR>\n" );
document.write( "e^2x = 3 or e^2x = -2<BR>\n" );
document.write( "Take the natural log to get:<BR>\n" );
document.write( "2x = ln3 or 2x = ln(-2)<BR>\n" );
document.write( "x = (1/2)ln(3)  and there is no ln of a negative number.<BR>\n" );
document.write( "x = (1/2)*1.0986122..<BR>\n" );
document.write( "x = 0.549306..<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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