document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199909>Question 1199909</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the pair of integers (a,b) for which 2^a+1 + 2^a = 3^b+2 - 3^b </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834054 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=834054\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'm assuming the equation is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%28a%2B1%29%2B2%5Ea+=+3%5E%28b%2B2%29-3%5Eb ALIGN=MIDDLE  ALT=\"2%5E%28a%2B1%29%2B2%5Ea+=+3%5E%28b%2B2%29-3%5Eb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is equivalent to writing out 2^(a+1)+2^a = 3^(b+2)-3^b<BR>\n" );
document.write( "Use parenthesis for the exponents \"a+1\" and \"b+2\"\r<BR>\n" );
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document.write( "If my initial assumption is correct, then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%28a%2B1%29%2B2%5Ea+=+3%5E%28b%2B2%29-3%5Eb ALIGN=MIDDLE  ALT=\"2%5E%28a%2B1%29%2B2%5Ea+=+3%5E%28b%2B2%29-3%5Eb\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ea%2A2%5E1%2B2%5Ea+=+3%5Eb%2A3%5E2-3%5Eb ALIGN=MIDDLE  ALT=\"2%5Ea%2A2%5E1%2B2%5Ea+=+3%5Eb%2A3%5E2-3%5Eb\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the rule a^(b+c) = a^b*a^c\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ea%2A%282%2B1%29+=+3%5Eb%2A%289-1%29 ALIGN=MIDDLE  ALT=\"2%5Ea%2A%282%2B1%29+=+3%5Eb%2A%289-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A2%5Ea+=+8%2A3%5Eb ALIGN=MIDDLE  ALT=\"3%2A2%5Ea+=+8%2A3%5Eb\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%28a-3%29+=+3%5E%28b-1%29 ALIGN=MIDDLE  ALT=\"2%5E%28a-3%29+=+3%5E%28b-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Because the bases are different, the two sides are only equal when the exponents are zero (to make both sides to simplify to 1).<BR>\n" );
document.write( "a-3 = 0 leads to a = 3<BR>\n" );
document.write( "b-1 = 0 leads to b = 1<BR>\n" );
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