document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=244998>Question 244998</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given log(base a)x=4, log(base a)y=3, and log(base a)z=2 for constants x, y,z. find the value of the logarithm.\r<BR>\n" );
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document.write( "log(base a)((5th root of y^3 times x^6 times z^4)/(5th root of z^6 times x^2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #179123 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=179123\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you are given:\r<BR>\n" );
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document.write( "log(a,x) = 4<BR>\n" );
document.write( "log(a,y) = 3<BR>\n" );
document.write( "log(a,z) = 2\r<BR>\n" );
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document.write( "you want to find:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C%28%28%28root%285%2Cy%5E3%2Ax%5E6%2Az%5E4%29%29%29%2F%28root%285%2C%28z%5E6%2Ax%5E2%29%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28n%2Ca%29%2Froot%28n%2Cb%29+=+root%28n%2C%28a%2Fb%29%29 ALIGN=MIDDLE  ALT=\"root%28n%2Ca%29%2Froot%28n%2Cb%29+=+root%28n%2C%28a%2Fb%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, your equation becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C%28%28root%285%2C%28y%5E3%2Ax%5E6%2Az%5E4%29%2F%28z%5E6%2Ax%5E2%29%29%29%29%29 ALIGN=MIDDLE  ALT=\"log%28a%2C%28%28root%285%2C%28y%5E3%2Ax%5E6%2Az%5E4%29%2F%28z%5E6%2Ax%5E2%29%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%285%2Ca%29+=+a%5E%281%2F5%29 ALIGN=MIDDLE  ALT=\"root%285%2Ca%29+=+a%5E%281%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, your equation becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C%28%28%28y%5E3%2Ax%5E6%2Az%5E4%29%2F%28z%5E6%2Ax%5E2%29%29%5E%281%2F5%29%29%29%29 ALIGN=MIDDLE  ALT=\"log%28a%2C%28%28%28y%5E3%2Ax%5E6%2Az%5E4%29%2F%28z%5E6%2Ax%5E2%29%29%5E%281%2F5%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since log(a^b) = b*(log(a), your equation becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F5%29+%2A+log%28a%2C%28%28%28y%5E3%2Ax%5E6%2Az%5E4%29%2F%28z%5E6%2Ax%5E2%29%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since log(a/b) = log(a)/log(b), your equation becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F5%29+%2A+%28log%28a%2C%28y%5E3%2Ax%5E6%2Az%5E4%29%29+-+log%28a%2C%28z%5E6%2Ax%5E2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since log(a*b) = log(a) + log(b), your equation becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F5%29+%2A+%28log%28a%2C%28y%5E3%29%29+%2B+log%28a%2C%28x%5E6%29%29+%2B+log%28a%2C%28z%5E4%29%29+-+log%28a%2C%28z%5E6%29%29+-+log%28a%2C%28x%5E2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since log(a^b) = b*log(a), your equation becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F5%29+%2A+%283%2Alog%28a%2C%28y%29%29+%2B+6%2Alog%28a%2C%28x%29%29+%2B+4%2Alog%28a%2C%28z%29%29+-+6%2Alog%28a%2C%28z%29%29+-+2%2Alog%28a%2C%28x%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "from here on it's just a straight substitution since you are given:\r<BR>\n" );
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document.write( "log(a,x) = 4<BR>\n" );
document.write( "log(a,y) = 3<BR>\n" );
document.write( "log(a,z) = 2\r<BR>\n" );
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document.write( "your equation of:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F5%29+%2A+%283%2Alog%28a%2C%28y%29%29+%2B+6%2Alog%28a%2C%28x%29%29+%2B+4%2Alog%28a%2C%28z%29%29+-+6%2Alog%28a%2C%28z%29%29+-+2%2Alog%28a%2C%28x%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F5%29+%2A+%283%2A3+%2B+6%2A4+%2B+4%2A2+-+6%2A2+-+2%2A4%29 ALIGN=MIDDLE  ALT=\"%281%2F5%29+%2A+%283%2A3+%2B+6%2A4+%2B+4%2A2+-+6%2A2+-+2%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F5%29+%2A+%289%2B24%2B8-12-8%29 ALIGN=MIDDLE  ALT=\"%281%2F5%29+%2A+%289%2B24%2B8-12-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F5%29+%2A+%2821%29 ALIGN=MIDDLE  ALT=\"%281%2F5%29+%2A+%2821%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%2F5 ALIGN=MIDDLE  ALT=\"21%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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