document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140058>Question 1140058</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 2^x = 4^y = 8^z and 1/(2x) = 1/(4y) = 1/(8z) = 22/7. Show that x = 7/16, y = 7/32 and z = 7/48. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760524 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=760524\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ex+=+4%5Ey+=+8%5Ez ALIGN=MIDDLE  ALT=\"2%5Ex+=+4%5Ey+=+8%5Ez\"   DISABLED_style= \"max-width:90%; height:auto;\" > and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F%282x%29+=+1%2F%284y%29+=+1%2F%288z%29+=+22%2F7 ALIGN=MIDDLE  ALT=\"+1%2F%282x%29+=+1%2F%284y%29+=+1%2F%288z%29+=+22%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>doesn't make sense, here must be the sum:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F%282x%29%2B1%2F%284y%29+%2B+1%2F%288z%29+=+22%2F7 ALIGN=MIDDLE  ALT=\"+1%2F%282x%29%2B1%2F%284y%29+%2B+1%2F%288z%29+=+22%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " Show that:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+7%2F16 ALIGN=MIDDLE  ALT=\"x+=+7%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+7%2F32 ALIGN=MIDDLE  ALT=\"y+=+7%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+7%2F48 ALIGN=MIDDLE  ALT=\"z+=+7%2F48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We know <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E0 ALIGN=MIDDLE  ALT=\"x%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C%3E0 ALIGN=MIDDLE  ALT=\"y%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%3C%3E0 ALIGN=MIDDLE  ALT=\"z%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > because otherwise they would make the denominators zero, and the expression <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%282x%29+%2B+1%2F%284y%29+%2B+1%2F%288z%29 ALIGN=MIDDLE  ALT=\"1%2F%282x%29+%2B+1%2F%284y%29+%2B+1%2F%288z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > would not exist as a real number.\r<BR>\n" );
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document.write( "As <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=2%5E2 ALIGN=MIDDLE  ALT=\"4=2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8=2%5E3 ALIGN=MIDDLE  ALT=\"8=2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > , if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ex+=+4%5Ey+=+8%5Ez ALIGN=MIDDLE  ALT=\"2%5Ex+=+4%5Ey+=+8%5Ez\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ex+=+4%5Ey+=+%282%5E2%29%5Ey+=+2%5E%282y%29 ALIGN=MIDDLE  ALT=\"2%5Ex+=+4%5Ey+=+%282%5E2%29%5Ey+=+2%5E%282y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%282y%29%2F2%5Ex=2%5E%282y-x%29=1+meaning+that+%7B%7B%7B2y-x=0 ALIGN=MIDDLE  ALT=\"2%5E%282y%29%2F2%5Ex=2%5E%282y-x%29=1+meaning+that+%7B%7B%7B2y-x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2y ALIGN=MIDDLE  ALT=\"x=2y\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29x ALIGN=MIDDLE  ALT=\"y=%281%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ex+=+8%5Ez+=+%282%5E3%29%5Ez+=+2%5E%283z%29 ALIGN=MIDDLE  ALT=\"2%5Ex+=+8%5Ez+=+%282%5E3%29%5Ez+=+2%5E%283z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3z ALIGN=MIDDLE  ALT=\"x=3z\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%281%2F3%29x ALIGN=MIDDLE  ALT=\"z=%281%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
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document.write( "You could also talk about taking logarithms base 2.\ to get to the same conclusions.\r<BR>\n" );
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document.write( "Then, substituting into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%282x%29+%2B+1%2F%284y%29+%2B+1%2F%288z%29+=+22%2F7 ALIGN=MIDDLE  ALT=\"1%2F%282x%29+%2B+1%2F%284y%29+%2B+1%2F%288z%29+=+22%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%282x%29+%2B+1%2F%284%281%2F2%29x%29+%2B+1%2F%288z%29+=+22%2F7 ALIGN=MIDDLE  ALT=\"1%2F%282x%29+%2B+1%2F%284%281%2F2%29x%29+%2B+1%2F%288z%29+=+22%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%282x%29+%2B+1%2F%282x%29+%2B+1%2F%288z%29+=+22%2F7 ALIGN=MIDDLE  ALT=\"1%2F%282x%29+%2B+1%2F%282x%29+%2B+1%2F%288z%29+=+22%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx+%2B+1%2F%288z%29+=+22%2F7 ALIGN=MIDDLE  ALT=\"1%2Fx+%2B+1%2F%288z%29+=+22%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%283z%29+%2B+1%2F%288z%29+=+22%2F7 ALIGN=MIDDLE  ALT=\"1%2F%283z%29+%2B+1%2F%288z%29+=+22%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiplying both sides of the equation times the non-zero number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A8%2A7%2Az ALIGN=MIDDLE  ALT=\"3%2A8%2A7%2Az\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "we get the equivalent equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A7%2B3%2A7=22%2A3%2A8%2Az ALIGN=MIDDLE  ALT=\"8%2A7%2B3%2A7=22%2A3%2A8%2Az\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2B3%29%2A7=22%2A3%2A8%2Az ALIGN=MIDDLE  ALT=\"%288%2B3%29%2A7=22%2A3%2A8%2Az\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2A7=2%2A11%2A3%2A8%2Az ALIGN=MIDDLE  ALT=\"11%2A7=2%2A11%2A3%2A8%2Az\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F%282%2A3%2A8%29=z ALIGN=MIDDLE  ALT=\"7%2F%282%2A3%2A8%29=z\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28z=7%2F48%29 ALIGN=MIDDLE  ALT=\"highlight%28z=7%2F48%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then, as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3z ALIGN=MIDDLE  ALT=\"x=3z\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2A7%2F%282%2A3%2A8%29=7%2F%282%2A8%29=highlight%287%2F16%29 ALIGN=MIDDLE  ALT=\"x=3%2A7%2F%282%2A3%2A8%29=7%2F%282%2A8%29=highlight%287%2F16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29x ALIGN=MIDDLE  ALT=\"y=%281%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29%2A%287%2F16%29=highlight%287%2F32%29 ALIGN=MIDDLE  ALT=\"y=%281%2F2%29%2A%287%2F16%29=highlight%287%2F32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );