document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=47776>Question 47776</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact solution to the equation 3^x+5 = 9^x. I am having difficulty working this one out. Please be so kind as to help me with this problem. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #31595 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=31595\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3^x+5 = 9^x\r<BR>\n" );
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document.write( "9^x-3^x-5=0<BR>\n" );
document.write( "(3^x)^(2) - 3^x -5 = 0\r<BR>\n" );
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document.write( "This is a quadratic where the variable is 3^x<BR>\n" );
document.write( "Let 3^x = w, then rewrite the problem as:<BR>\n" );
document.write( "w^2 - w -5 =0<BR>\n" );
document.write( "Use the quadratic formula to get the following:<BR>\n" );
document.write( "w=[1+-sqrt(1+20)]/2<BR>\n" );
document.write( "w=[1+-sqrt(21)]/2\r<BR>\n" );
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document.write( "Now, reverting back to the fact that w=3^x you get:<BR>\n" );
document.write( "3^x=[1+-sqrt(21)]/2<BR>\n" );
document.write( "3^x=2.79128785... or 3^x is a negative number( which it cannot be)<BR>\n" );
document.write( "Take the log to get:<BR>\n" );
document.write( "xlog3 =2.79128785...<BR>\n" );
document.write( "The x=5.85026934...<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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