document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=798721>Question 798721</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Most photocopiers can reduce the size an image by a maximum of 64% of the original dimensions how many reductions at the maximum setting would it take to reduce an image to less than 10% of its original dimensions\r<BR>\n" );
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document.write( "I did it logically and I got a answer of 6 <BR>\n" );
document.write( "But I prefer to do it algebraically using the geometric sequence formula<BR>\n" );
document.write( "Show me !!\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #482527 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=482527\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> With each reduction, the previous dimensions get multiplied by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.64=64%2F100=%2264%25%22 ALIGN=MIDDLE  ALT=\"0.64=64%2F100=%2264%25%22\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "With <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > reductions the original dimensions will be multiplied times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.64%5En ALIGN=MIDDLE  ALT=\"0.64%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "and they will end up being multiplied times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%220.10%22=10%2F100=%2210+%25%22 ALIGN=MIDDLE  ALT=\"%220.10%22=10%2F100=%2210+%25%22\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.64%5En%3C0.10 ALIGN=MIDDLE  ALT=\"0.64%5En%3C0.10\"   DISABLED_style= \"max-width:90%; height:auto;\" > is our equation\r<BR>\n" );
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document.write( "We could say that thew original length would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B0%5D ALIGN=MIDDLE  ALT=\"b%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "and the length of the nth reduction would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5Bn%5D=b%5B0%5D%2A0.64%5En ALIGN=MIDDLE  ALT=\"b%5Bn%5D=b%5B0%5D%2A0.64%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then we could write that a 10% reduction would reduce <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B0%5D ALIGN=MIDDLE  ALT=\"b%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B0%5D%2A0.1 ALIGN=MIDDLE  ALT=\"b%5B0%5D%2A0.1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "and write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B0%5D%2A0.64%5En%3Cb%5B0%5D%2A0.1 ALIGN=MIDDLE  ALT=\"b%5B0%5D%2A0.64%5En%3Cb%5B0%5D%2A0.1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.64%5En%3C0.10 ALIGN=MIDDLE  ALT=\"0.64%5En%3C0.10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "From there we can<BR>\n" );
document.write( "either start calculating powers of 0.64 until we get to less than 0.1,<BR>\n" );
document.write( "or use logarithms.<BR>\n" );
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document.write( "Calculating powers:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.64%5E2=0.4096 ALIGN=MIDDLE  ALT=\"0.64%5E2=0.4096\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.64%5E3=0.262144 ALIGN=MIDDLE  ALT=\"0.64%5E3=0.262144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.64%5E4=0.167772 ALIGN=MIDDLE  ALT=\"0.64%5E4=0.167772\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.64%5E5=0.107374 ALIGN=MIDDLE  ALT=\"0.64%5E5=0.107374\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.64%5E6=0.0687194 ALIGN=MIDDLE  ALT=\"0.64%5E6=0.0687194\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Using logarithms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.64%5En%3C0.10 ALIGN=MIDDLE  ALT=\"0.64%5En%3C0.10\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%280.64%5En%29%3Clog%280.10%29 ALIGN=MIDDLE  ALT=\"log%280.64%5En%29%3Clog%280.10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Alog%280.64%29%3C-1 ALIGN=MIDDLE  ALT=\"n%2Alog%280.64%29%3C-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Alog%280.64%29%3C-1 ALIGN=MIDDLE  ALT=\"n%2Alog%280.64%29%3C-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%280.64%29=approximately ALIGN=MIDDLE  ALT=\"log%280.64%29=approximately\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.19382%3C0 ALIGN=MIDDLE  ALT=\"-0.19382%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Dividing both sides of the inequality by a negative number, the inequality sign reverses, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Alog%280.64%29%3C-1 ALIGN=MIDDLE  ALT=\"n%2Alog%280.64%29%3C-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%3E-1%2Flog%280.64%29=approximately ALIGN=MIDDLE  ALT=\"n%3E-1%2Flog%280.64%29=approximately\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.16 ALIGN=MIDDLE  ALT=\"5.16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since we need an integer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we need <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%3E=6 ALIGN=MIDDLE  ALT=\"n%3E=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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