document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=997511>Question 997511</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am stuck on this one.  Any help will be appreciated!  e^x-4e^(-x)=3  x=ln4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615550 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=615550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> start with e^x - 4e^(-x) = 3\r<BR>\n" );
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document.write( "since e^(-x) is the equivalent to 1/e^x, the equation becomes:\r<BR>\n" );
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document.write( "e^x - 4/(e^x) = 3\r<BR>\n" );
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document.write( "multiply both sides of this equation by e^x and you get:\r<BR>\n" );
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document.write( "e^x * e^x - 4 = 3 * e^x\r<BR>\n" );
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document.write( "e^x * e^x is the same as e^(x+x) is the same as e^(2x) which is the same as (e^x)^2.\r<BR>\n" );
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document.write( "your equation becomes (e^x)^2 - 4 = 3 * e^x\r<BR>\n" );
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document.write( "subtract 3 * e^x from both sides of this equation to get (e^x)^2 - 3e^x - 4 = 0\r<BR>\n" );
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document.write( "let y = e^x and the equation becomes y^2 - 3y - 4 = 0\r<BR>\n" );
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document.write( "this is a quadratic equation that can be factored to get (y - 4) * (y + 1) = 0\r<BR>\n" );
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document.write( "solve for y to get y = 4 or y = -1.\r<BR>\n" );
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document.write( "since y = e^x, replace y to get:\r<BR>\n" );
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document.write( "e^x = 4 or e^x = -1\r<BR>\n" );
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document.write( "e^x = 4 if and only if ln(4) = x\r<BR>\n" );
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document.write( "this matches the solution you showed, so this is the correct answer.\r<BR>\n" );
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document.write( "e^x = -1 if and only if ln(-1) = x\r<BR>\n" );
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document.write( "since you cannot take the log of a negative number, this solution is invalid.\r<BR>\n" );
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document.write( "your only solution is x = ln(4).\r<BR>\n" );
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document.write( "you could also have stopped at e^x = -1 since y = e^x is only valid for positive values of y.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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