document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1022712>Question 1022712</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is e^x - 5e^-x - 4 = 0\r<BR>\n" );
document.write( "\n" );
document.write( "how to get the appropriate answer hehehe thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #638326 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=638326\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> start with e^x - 5e^-x - 4 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since e^-x is the same as 1/e^x, this becomes e^x - 5/e^x - 4 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply both sides of that equation by e^x to get (e^x)^2 - 5 - 4e^x = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "reorder the terms in descending order of degree to get (e^x)^2 - 4e^x - 5 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is a quadratic equation where the argument of the function is e^x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let some other variable name be equal to e^x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i'll use the variable name of b.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the equation becomes b^2 - 4b - 5 = 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now it's easier to see that it is a quadratic equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "factor this quadratic to get (b-5) * (b+1) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for b to get b = 5 or b = -1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since b is equal to e^x, this becomes e^x = 5 or e^x = -1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for x in each of these equations by taking the natural log of both sides of each equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you will get ln(e^x) = ln(5) or ln(e^x) = ln(-1).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since you cannot take the log of a negative number and get a real answer, then the only viable solution is ln(e^x) = ln(5).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since ln(e^x) is the same as x * ln(e) and since ln(e) is equal to 1, then you get ln(e^x) is equal to x * 1 which is equal to x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your equation becomes x = ln(5).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's your solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can go one step further by finding the natural log of 5 to get x = 1.609437912.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = ln(5) is the exact solution.<BR>\n" );
document.write( "x = 1.609437912 is an approximate solution since it does not appear that ln(5) results in a rational number.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );