document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136697>Question 1136697</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the one to one property to solve the equations for x \r<BR>\n" );
document.write( "\n" );
document.write( "A) log 11=log (x^2+7)\r<BR>\n" );
document.write( "\n" );
document.write( "B)e ^x^2-3=e^2x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754498 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=754498\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a.)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "log(11) = log(x^2 + 7)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is true if and only if 11 = x^2 + 7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 7 from both sides to get 4 = x^2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for x to get x = plus or minus 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when x = plus or minus 2, x^2 is 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "log(11) = log(x^2 + 7) becomes log(11) = log(4 + 7) which becomes log(11) = log(11) which confirms the solution is good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b.)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "e^(x^2-3) = e^(2x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is true if and only if x^2 - 3 = 2x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 2x from both sides to get x^2 - 2x - 3 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "factor to get (x-3) * (x+1) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for x to get x = -1 or x = 3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when x = -1, e^(x^2-3) = e^(2x) becomes e^(1-3) = e^(2*-1) which becomes e^(-2) = e^(-2) which confirms the solution is good. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when x = 3, e^(x^2-3) = e^(2x) becomes e^(9-3) = e^(2*3) which becomes e^(6) = e^(6) which confirms the solution is good.\r<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" );