document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133341>Question 133341</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the unknown in the equation \r<BR>\n" );
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document.write( "log3(3^m+1 plus 3^m+2) = log3 972\r<BR>\n" );
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document.write( "Im am having trouble getting to the answer which is m = 4\r<BR>\n" );
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document.write( "Please note that the 3 in the log 3 972 is small </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97528 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=97528\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C%283%5E%28m%2B1%29%2B3%5E%28m%2B2%29%29%29=+log%283%2C%28972%29%29 ALIGN=MIDDLE  ALT=\"log%283%2C%283%5E%28m%2B1%29%2B3%5E%28m%2B2%29%29%29=+log%283%2C%28972%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E%28log%283%2C%283%5E%28m%2B1%29%2B3%5E%28m%2B2%29%29%29%29=+3%5E%28log%283%2C%28972%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Raise both sides as exponents with bases of 3. This will eliminate the logs\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E%28m%2B1%29%2B3%5E%28m%2B2%29=+972 ALIGN=MIDDLE  ALT=\"3%5E%28m%2B1%29%2B3%5E%28m%2B2%29=+972\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E%28m%29%2A3%5E%281%29%2B3%5E%28m%29%2A3%5E%282%29=+972 ALIGN=MIDDLE  ALT=\"3%5E%28m%29%2A3%5E%281%29%2B3%5E%28m%29%2A3%5E%282%29=+972\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the left side using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28y%2Bz%29=x%5Ey%2Ax%5Ez ALIGN=MIDDLE  ALT=\"x%5E%28y%2Bz%29=x%5Ey%2Ax%5Ez\"   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%5E%28m%29%2A3%2B3%5E%28m%29%2A9=+972 ALIGN=MIDDLE  ALT=\"3%5E%28m%29%2A3%2B3%5E%28m%29%2A9=+972\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E1 ALIGN=MIDDLE  ALT=\"3%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 3. Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2 ALIGN=MIDDLE  ALT=\"3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 9\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A3%5E%28m%29%281%2B3%29=+972 ALIGN=MIDDLE  ALT=\"3%2A3%5E%28m%29%281%2B3%29=+972\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A3%5E%28m%29%284%29=+972 ALIGN=MIDDLE  ALT=\"3%2A3%5E%28m%29%284%29=+972\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A3%5E%28m%29=+243 ALIGN=MIDDLE  ALT=\"3%2A3%5E%28m%29=+243\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E%28m%29=+81 ALIGN=MIDDLE  ALT=\"3%5E%28m%29=+81\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E%28m%29=+3%5E4 ALIGN=MIDDLE  ALT=\"3%5E%28m%29=+3%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite 81 as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E4 ALIGN=MIDDLE  ALT=\"3%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the bases are equal, this means that the exponents are equal. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=4 ALIGN=MIDDLE  ALT=\"m=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=4 ALIGN=MIDDLE  ALT=\"m=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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