document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107094>Question 107094</A>: <I><SPAN STYLE=\"word-break: break-all;\"> express as a single log: 1/2loga x + 4loga y -1/3loga z </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77926 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=77926\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's look at what we know about logarithms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=loga%28x%5En%29=n%2Aloga%28x%29 ALIGN=MIDDLE  ALT=\"loga%28x%5En%29=n%2Aloga%28x%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=loga%28x%29+%2B+loga%28y%29+=+loga%28x%2Ay%29 ALIGN=MIDDLE  ALT=\"loga%28x%29+%2B+loga%28y%29+=+loga%28x%2Ay%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=loga%28x%29+-+loga%28y%29+=+loga%28x%2Fy%29 ALIGN=MIDDLE  ALT=\"loga%28x%29+-+loga%28y%29+=+loga%28x%2Fy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using these facts, let's operate on your orignial expression:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29loga%28x%29+%2B+4%2Aloga%28y%29+-%281%2F3%29loga%28z%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29loga%28x%29+%2B+4%2Aloga%28y%29+-%281%2F3%29loga%28z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Beginning with the first term, remember that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%281%2F2%29=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"x%5E%281%2F2%29=sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29loga%28x%29=loga%28sqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29loga%28x%29=loga%28sqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Similarly, the other two terms become:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Aloga%28y%29=loga%28y%5E4%29 ALIGN=MIDDLE  ALT=\"4%2Aloga%28y%29=loga%28y%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29loga%28z%29+=+loga%28z%5E%281%2F3%29%29 ALIGN=MIDDLE  ALT=\"%281%2F3%29loga%28z%29+=+loga%28z%5E%281%2F3%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=z%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"z%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the cube root of z, but I can't render that on this system)\r<BR>\n" );
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document.write( "Putting the terms together, using the second rule from above:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=loga%28%28y%5E4%29%2Asqrt%28x%29%2Fz%5E%281%2F3%29%29 ALIGN=MIDDLE  ALT=\"loga%28%28y%5E4%29%2Asqrt%28x%29%2Fz%5E%281%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The answer would be much neater if I could replace the fractional power on z with a cube root radical, but it is still correct in this form. </SPAN>\n" );
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