document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=222910>Question 222910</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear Sir:<BR>\n" );
document.write( "   I am trying to solve the following equation for x:\r<BR>\n" );
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document.write( "     y = {e^x} / {1 + 2e^x}\r<BR>\n" );
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document.write( "I have tried various approaches but they do not seem to work:<BR>\n" );
document.write( "    (1) multiplying both sides of the equation by the value of the denominator and then taking the logarithms of both sides. <BR>\n" );
document.write( "    (2) rewriting the equation using fractional exponents and then trying to simplify the right hand side before taking the logarithm of both sides<BR>\n" );
document.write( "But, of course when I take the logarithm of both sides I cannot separate the expression in the parenthesis. Obviously, I am on the wrong track, but I have not found any help in my math books or my professor's notes.<BR>\n" );
document.write( "Is it possible for you to help me. I would be very grateful for advise and an illustration of the appropriate method.<BR>\n" );
document.write( "     Very truly yours,<BR>\n" );
document.write( "     Lawrence G. Lever (an older student returning to mathematics after many years)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #166784 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=166784\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y = {e^x} / {1 + 2e^x} <BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Cross multiply to get:<BR>\n" );
document.write( "y + 2ye^x = e^x<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Get the e^x terms together:<BR>\n" );
document.write( "2ye^x-e^x = -y<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Factor out the e^x:<BR>\n" );
document.write( "e^x(2y-1) = -y<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Divide thru by 2y-1 to get<BR>\n" );
document.write( "e^x = -y/(2y-1)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Take the natural log to solve for x<BR>\n" );
document.write( "x = ln[-y/(2y-1)]<BR>\n" );
document.write( "===========================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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