document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=54932>Question 54932</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me wit this problem:<BR>\n" );
document.write( "Find the exact solution to the equation 3^x+5=9^x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #37139 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=37139\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3^x+5=9^x<BR>\n" );
document.write( "Rewrite as:<BR>\n" );
document.write( "3^(2x)-3^x-5=0<BR>\n" );
document.write( "Let 3^x be \"w\"<BR>\n" );
document.write( "Rewrite the equation in \"w\", as follows:<BR>\n" );
document.write( "w^2-w-5=0<BR>\n" );
document.write( "Use the quadratic formula to solve for \"w\", as follows:<BR>\n" );
document.write( "w=[1+-sqrt(1+20)]/2<BR>\n" );
document.write( "w=[1+-sqrt(21)]/2<BR>\n" );
document.write( "Convert back to \"x\" notation.<BR>\n" );
document.write( "3^x=[1+-sqrt(21)]/2<BR>\n" );
document.write( "Take the log of both sides to get:<BR>\n" );
document.write( "x(log 3)=[1+-sqrt(21)]/2<BR>\n" );
document.write( "x=[1+-sqrt(21)/[2log(3)]<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );