document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1075852>Question 1075852</A>: <I><SPAN STYLE=\"word-break: break-all;\"> using substitution y3^x solve the equation 3^x=2x+3^-x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #690495 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52866)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=690495\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "using substitution y3^x solve the equation 3^x=2x+3^-x<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In this case I will not use the substitution (since in this case it doesn't work at all).\r<BR>\n" );
document.write( "\n" );
document.write( "I will use my common sense.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "See the plot below, which shows the left side and the right side functions separately.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+330%2C+330%2C+-1.5%2C+1.5%2C+-1.5%2C+2.5%2C%0D%0A++++++++++3%5Ex%2C+2x+%2B+3%5E%28-x%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Plots y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5Ex ALIGN=MIDDLE  ALT=\"3%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3%5E%28-x%29 ALIGN=MIDDLE  ALT=\"2x%2B3%5E%28-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Looking into the plot, you can see immediately that x = 0 is the solution.<BR>\n" );
document.write( "By finding the root visually, you can check it formally: it works.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Also, the plot gives you a clue that the equation has no other roots.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );