document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=560634>Question 560634</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9%5Ex%2B6%5Ex=2%5E%282x%2B1%29+ ALIGN=MIDDLE  ALT=\"+9%5Ex%2B6%5Ex=2%5E%282x%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #364140 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=364140\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = 0 works, but we need to prove it is the only solution. Note that we can write the equation as\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 9^x + 6^x = 2(4^x)\">\r<BR>\n" );
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document.write( "Dividing both sides by 4^x,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (\frac{9}{4})^x + (\frac{6}{4})^x = 2\">\r<BR>\n" );
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document.write( "As you can see, the LHS is a strictly increasing function of x (bijective or one-to-one), so there can only be one value of x in which the LHS equals 2. We have already found it to be x=0. </SPAN>\n" );
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