document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=631098>Question 631098</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have tried and tried on this problem and just cant get it right. I even had a tutor online help me and they got it wrong too... this is the problem ...\r<BR>\n" );
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document.write( "Solve the system of equations. Round approximate values to the nearest ten-thousandth. \r<BR>\n" );
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document.write( "y = log2x<BR>\n" );
document.write( "y = x&#8722;5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #397461 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=397461\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Maybe something in the problem got \"lost in translation.\"<BR>\n" );
document.write( "For example, I wonder if you meant<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=log%28%282x%29%29 ALIGN=MIDDLE  ALT=\"y=log%28%282x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the first function,<BR>\n" );
document.write( "or maybe it was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=log%282%2Cx%29 ALIGN=MIDDLE  ALT=\"y=log%282%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The answer would depend on what that first function is.<BR>\n" );
document.write( "In either of those cases, the log function and the y=x-5 function graphs will cross at two points, like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-1%2C9%2C-6%2C4%2Cx-5%2Clog%282%2Cx%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-1%2C9%2C-6%2C4%2Cx-5%2Clog%282%2Cx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so you would have 2 solutions (which I will show you further down).<BR>\n" );
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document.write( "It could also be that the problem is neither of those, and something in the problem is irretrievably \"lost in translation.\"<BR>\n" );
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document.write( "It could also be that the \"officially correct answer\" that you were given is wrong, or that it needs to be entered in a specific format. After seeing my youngest child through (online) high school courses, I would not be surprised. Sometimes the official answer was wrong, and sometimes the computer would accept only (8,3), but not (8, 3) or the other way around.<BR>\n" );
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document.write( "If it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=log%282x%29 ALIGN=MIDDLE  ALT=\"y=log%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.00001 ALIGN=MIDDLE  ALT=\"x=0.00001\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.00001-5=-4.99999 ALIGN=MIDDLE  ALT=\"0.00001-5=-4.99999\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2A0.00001%29=log%280.00002%29=-5.000000 ALIGN=MIDDLE  ALT=\"log%282%2A0.00001%29=log%280.00002%29=-5.000000\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282x%29%3Ex-5 ALIGN=MIDDLE  ALT=\"log%282x%29%3Ex-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > but they are very close.<BR>\n" );
document.write( "For a smaller x, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.000005 ALIGN=MIDDLE  ALT=\"x=0.000005\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.000005-5=-4.999995 ALIGN=MIDDLE  ALT=\"0.000005-5=-4.999995\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2A0.000005%29=log%280.00001%29=-5.000000 ALIGN=MIDDLE  ALT=\"log%282%2A0.000005%29=log%280.00001%29=-5.000000\"   DISABLED_style= \"max-width:90%; height:auto;\" > , with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282x%29%3Cx-5 ALIGN=MIDDLE  ALT=\"log%282x%29%3Cx-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > but they and very close.<BR>\n" );
document.write( "That means that the answer for x must be a number in between, that I would round to 0.00001 if I was allowed, but it rounds to 0.0000 when rounded to the nearest ten-thousandth.<BR>\n" );
document.write( "The answer for y is -5.0000 when rounded to the nearest ten-thousandth, because for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.00001 ALIGN=MIDDLE  ALT=\"x=0.00001\"   DISABLED_style= \"max-width:90%; height:auto;\" >, for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.000005 ALIGN=MIDDLE  ALT=\"x=0.000005\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and for everything in between, the values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282x%29 ALIGN=MIDDLE  ALT=\"log%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5 ALIGN=MIDDLE  ALT=\"x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > rounds to -5.0000.<BR>\n" );
document.write( "That solution would be expressed as (0.0000, -5.0000).<BR>\n" );
document.write( "On the other end, I found that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6.0853 ALIGN=MIDDLE  ALT=\"x=6.0853\"   DISABLED_style= \"max-width:90%; height:auto;\" > seemed to be the closest I could get, with<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.0853-5=1.0853 ALIGN=MIDDLE  ALT=\"6.0853-5=1.0853\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2A6.0853%29=log%2812.1706%29 ALIGN=MIDDLE  ALT=\"log%282%2A6.0853%29=log%2812.1706%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=1.0853 (rounded).<BR>\n" );
document.write( "That would give you the (x, y) pair (6.0853, 1.0853).<BR>\n" );
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document.write( "If it was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=log%282%2Cx%29 ALIGN=MIDDLE  ALT=\"y=log%282%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8 ALIGN=MIDDLE  ALT=\"x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3 ALIGN=MIDDLE  ALT=\"y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or (3, 2) is a nice exact answer. Another solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.031949781 ALIGN=MIDDLE  ALT=\"x=0.031949781\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4.968052 ALIGN=MIDDLE  ALT=\"y=-4.968052\"   DISABLED_style= \"max-width:90%; height:auto;\" > which rounded gives you the pair (0.0319, -4.9681). </SPAN>\n" );
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