document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=26344>Question 26344</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If y = 9, find the integral values of x and z that satisfy all of the following equations:<BR>\n" );
document.write( "z^x = y^2x<BR>\n" );
document.write( "2^z = (2)(4^x)<BR>\n" );
document.write( "x+y+z = 16\r<BR>\n" );
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document.write( "I'd really appreciate the help! Thanks in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #14193 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=14193\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ignoring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5Ex+=+y%5E2x ALIGN=MIDDLE  ALT=\"z%5Ex+=+y%5E2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > for now, lets look at the other 2 equations.\r<BR>\n" );
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document.write( "We can take logs to the base2 with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ez+=+%282%29%284%5Ex%29 ALIGN=MIDDLE  ALT=\"2%5Ez+=+%282%29%284%5Ex%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. First this is rewritten as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ez+=+%282%29%282%5E%282x%29%29 ALIGN=MIDDLE  ALT=\"2%5Ez+=+%282%29%282%5E%282x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This then becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zlog2+=+log2+%2B+2xlog2 ALIGN=MIDDLE  ALT=\"zlog2+=+log2+%2B+2xlog2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now log2 to base2 is 1, so we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+1+%2B+2x ALIGN=MIDDLE  ALT=\"z+=+1+%2B+2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--> 2x - z = -1\r<BR>\n" );
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document.write( "x+y+z = 16<BR>\n" );
document.write( "x+9+z = 16<BR>\n" );
document.write( "--> x + z = 7\r<BR>\n" );
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document.write( "Add these 2 equations together and we get 3x = 6. Therefore x = 2.\r<BR>\n" );
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document.write( "Hence, from x+z = 7, we then know that z = 5.\r<BR>\n" );
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document.write( "So, we have x=2, z=5. Check these values in both of the original equations 2 and 3.\r<BR>\n" );
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document.write( "Now check in equation 1... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5Ex+=+y%5E2x ALIGN=MIDDLE  ALT=\"z%5Ex+=+y%5E2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2+=+9%5E4 ALIGN=MIDDLE  ALT=\"5%5E2+=+9%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ie 25 = 6561 which is clearly wrong. So either you copied one of the equations down wrong? or the answer is \"there is no solution to all 3 equations\".\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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