document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=975062>Question 975062</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A power function with form y= a x^p passes through the points (3, 2/81) and (6, 1/1296). Find the constants a and p\r<BR>\n" );
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document.write( "I found a=6 please tell me the value of p? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #596895 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=596895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+a%2Ax%5Ep ALIGN=MIDDLE  ALT=\"y=+a%2Ax%5Ep\"   DISABLED_style= \"max-width:90%; height:auto;\" > passes through the points (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F81 ALIGN=MIDDLE  ALT=\"2%2F81\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F1296 ALIGN=MIDDLE  ALT=\"1%2F1296\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Find the constants <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   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=y=+a%2Ax%5Ep ALIGN=MIDDLE  ALT=\"y=+a%2Ax%5Ep\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28y%29=+log%28a%2Ax%5Ep+%29 ALIGN=MIDDLE  ALT=\"log%28y%29=+log%28a%2Ax%5Ep+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28y%29=+log%28a%29%2Blog%28+x%5Ep+%29 ALIGN=MIDDLE  ALT=\"log%28y%29=+log%28a%29%2Blog%28+x%5Ep+%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%28y%29=+log%28a%29%2Bp%2Alog%28+x+%29 ALIGN=MIDDLE  ALT=\"log%28y%29=+log%28a%29%2Bp%2Alog%28+x+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if given the points : <BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2F81 ALIGN=MIDDLE  ALT=\"+2%2F81\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%2F81 ALIGN=MIDDLE  ALT=\"y=2%2F81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " and <BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F1296 ALIGN=MIDDLE  ALT=\"1%2F1296\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2F1296 ALIGN=MIDDLE  ALT=\"y=1%2F1296\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, we use them to form a system of equations\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28y%29=+log%28a%29%2Bp%2Alog%28+x+%29 ALIGN=MIDDLE  ALT=\"log%28y%29=+log%28a%29%2Bp%2Alog%28+x+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%2F81 ALIGN=MIDDLE  ALT=\"y=2%2F81\"   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%282%2F81%29=+log%28a%29%2Bp%2Alog%28+3+%29 ALIGN=MIDDLE  ALT=\"log%282%2F81%29=+log%28a%29%2Bp%2Alog%28+3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  .....eq.1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28y%29=+log%28a%29%2Bp%2Alog%28+x+%29 ALIGN=MIDDLE  ALT=\"log%28y%29=+log%28a%29%2Bp%2Alog%28+x+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2F1296 ALIGN=MIDDLE  ALT=\"y=1%2F1296\"   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%281%2F1296%29=+log%28a%29%2Bp%2Alog%28+6%29 ALIGN=MIDDLE  ALT=\"log%281%2F1296%29=+log%28a%29%2Bp%2Alog%28+6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   .....eq.2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%29-log%2881%29=+log%28a%29%2Bp%2Alog%28+3+%29 ALIGN=MIDDLE  ALT=\"log%282%29-log%2881%29=+log%28a%29%2Bp%2Alog%28+3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  .....eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%281%29-log%281296%29=+log%28a%29%2Bp%2Alog%28+6%29+ ALIGN=MIDDLE  ALT=\"log%281%29-log%281296%29=+log%28a%29%2Bp%2Alog%28+6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  .....eq.2..........write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81 ALIGN=MIDDLE  ALT=\"81\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1296 ALIGN=MIDDLE  ALT=\"1296\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E4%2A2%5E4 ALIGN=MIDDLE  ALT=\"3%5E4%2A2%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------------------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%29-log%283%5E4%29=+log%28a%29%2Bp%2Alog%28+3+%29 ALIGN=MIDDLE  ALT=\"log%282%29-log%283%5E4%29=+log%28a%29%2Bp%2Alog%28+3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  .....eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%281%29-log%283%5E4%2A2%5E4%29=+log%28a%29%2Bp%2Alog%28+2%2A3%29 ALIGN=MIDDLE  ALT=\"log%281%29-log%283%5E4%2A2%5E4%29=+log%28a%29%2Bp%2Alog%28+2%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   .....eq.2<BR>\n" );
document.write( "--------------------------------------------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%29-4log%283%29=+log%28a%29%2Bp%2Alog%28+3+%29 ALIGN=MIDDLE  ALT=\"log%282%29-4log%283%29=+log%28a%29%2Bp%2Alog%28+3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  .....eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%281%29-%28log%283%5E4%29%2Blog%282%5E4%29%29=+log%28a%29%2Bp%2A%28log%28+2%29%2Blog%283%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >   .....eq.2...substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%281%29=0 ALIGN=MIDDLE  ALT=\"log%281%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------------------------------------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%29-4log%283%29=+log%28a%29%2Bp%2Alog%28+3+%29 ALIGN=MIDDLE  ALT=\"log%282%29-4log%283%29=+log%28a%29%2Bp%2Alog%28+3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  .....eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0-4log%283%29-4log%282%29%29=+log%28a%29%2Bp%2A%28log%28+2%29%2Blog%283%29%29 ALIGN=MIDDLE  ALT=\"0-4log%283%29-4log%282%29%29=+log%28a%29%2Bp%2A%28log%28+2%29%2Blog%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   .....eq.2<BR>\n" );
document.write( "------------------------------------------------------------------subtract 1 from 2 \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4log%283%29-4log%282%29%29-log%282%29%2B4log%283%29=+log%28a%29%2Bp%2A%28log%28+2%29%2Blog%283%29%29-log%28a%29-p%2Alog%28+3+%29 ALIGN=MIDDLE   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=-5log%282%29=+p%2A%28log%28+2%29%2Blog%283%29-p%2Alog%28+3+%29%29 ALIGN=MIDDLE  ALT=\"-5log%282%29=+p%2A%28log%28+2%29%2Blog%283%29-p%2Alog%28+3+%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=-5log%282%29=+p%2Alog%28+2%29 ALIGN=MIDDLE  ALT=\"-5log%282%29=+p%2Alog%28+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-5 ALIGN=MIDDLE  ALT=\"p=-5\"   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%282%29-4log%283%29=+log%28a%29%2Bp%2Alog%28+3+%29 ALIGN=MIDDLE  ALT=\"log%282%29-4log%283%29=+log%28a%29%2Bp%2Alog%28+3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  .....eq.1...substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   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%282%29-4log%283%29=+log%28a%29-5%2Alog%28+3+%29+ ALIGN=MIDDLE  ALT=\"log%282%29-4log%283%29=+log%28a%29-5%2Alog%28+3+%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%282%29-4log%283%29%2B5%2Alog%28+3+%29+=+log%28a%29+ ALIGN=MIDDLE  ALT=\"log%282%29-4log%283%29%2B5%2Alog%28+3+%29+=+log%28a%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%282%29%2Blog%28+3+%29+=+log%28a%29+ ALIGN=MIDDLE  ALT=\"log%282%29%2Blog%28+3+%29+=+log%28a%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%282%2A3%29=+log%28a%29 ALIGN=MIDDLE  ALT=\"log%282%2A3%29=+log%28a%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%286%29=+log%28a%29+ ALIGN=MIDDLE  ALT=\"log%286%29=+log%28a%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=a=6 ALIGN=MIDDLE  ALT=\"a=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, your function is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+6x%5E%28-5%29 ALIGN=MIDDLE  ALT=\"y=+6x%5E%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+6%281%2Fx%5E5%29 ALIGN=MIDDLE  ALT=\"y=+6%281%2Fx%5E5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+6%2Fx%5E5 ALIGN=MIDDLE  ALT=\"y=+6%2Fx%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );