document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=161664>Question 161664</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I haven't done a problem like this for several years and I don't remember how to solve it! It's driving me crazy! Here is the problem:\r<BR>\n" );
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document.write( "1024=2^n-1. Solve for n.\r<BR>\n" );
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document.write( "I don't remember how to bring the exponent (n-1) down so that I can solve for n.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #119138 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=119138\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are at least two ways to solve this\r<BR>\n" );
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document.write( "Method #1:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1024=2%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"1024=2%5E%28n-1%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=2%5E10=2%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"2%5E10=2%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite 1,024 as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E10 ALIGN=MIDDLE  ALT=\"2%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This is possible since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E10=1024 ALIGN=MIDDLE  ALT=\"2%5E10=1024\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the bases are equal (they are both 2), this means that the exponents are equal. So \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10=n-1 ALIGN=MIDDLE  ALT=\"10=n-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the exponents equal to one another.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2B1=n%2Bcross%28-1%2B1%29 ALIGN=MIDDLE  ALT=\"10%2B1=n%2Bcross%28-1%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 1 to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11=n ALIGN=MIDDLE  ALT=\"11=n\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add.\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=11 ALIGN=MIDDLE  ALT=\"n=11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=================================================\r<BR>\n" );
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document.write( "Method #2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1024=2%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"1024=2%5E%28n-1%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=log%2810%2C%281024%29%29=log%2810%2C%282%5E%28n-1%29%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%281024%29%29=log%2810%2C%282%5E%28n-1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the log of both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%281024%29%29=%28n-1%29log%2810%2C%282%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%281024%29%29=%28n-1%29log%2810%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the right side using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%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=log%2810%2C%281024%29%29%2Flog%2810%2C%282%29%29=n-1 ALIGN=MIDDLE  ALT=\"log%2810%2C%281024%29%29%2Flog%2810%2C%282%29%29=n-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%282%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%282%29%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=10=n-1 ALIGN=MIDDLE  ALT=\"10=n-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%281024%29%29%2Flog%2810%2C%282%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%281024%29%29%2Flog%2810%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 10\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2B1=n%2Bcross%28-1%2B1%29 ALIGN=MIDDLE  ALT=\"10%2B1=n%2Bcross%28-1%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 1 to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11=n ALIGN=MIDDLE  ALT=\"11=n\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add.\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=11 ALIGN=MIDDLE  ALT=\"n=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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