document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167361>Question 167361</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following equation. Give exact answer to and a decimal aproximation to 2 decimal places of accuracy if needed.\r<BR>\n" );
document.write( "\n" );
document.write( "3^(2x)-20=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 #123326 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=123326\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the following equation. Give exact answer to and a decimal aproximation to 2 decimal places of accuracy if needed. <BR>\n" );
document.write( "3^(2x)-20=3^(x)<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Substitute y for 3^x<BR>\n" );
document.write( "y^2 - 20 = y  See that?<BR>\n" );
document.write( "y^2 - y - 20 = 0<BR>\n" );
document.write( "(y-5)*(y+4) = 0<BR>\n" );
document.write( "y = 5, y = -4<BR>\n" );
document.write( "Sub back 3^x for y<BR>\n" );
document.write( "3^x = 5<BR>\n" );
document.write( "x = log(5)/log(3) (exact)<BR>\n" );
document.write( "x = 1.47  (2 decimals)<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "3^x = -4 This is not possible, as no exponent of 3 will give a negative number (no real number will, there is a complex number that will).\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );