document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=206233>Question 206233</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write 3log u - log v - 4log z expression as a single logarithm </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #155802 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=155802\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your problem is stated as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Alog%28%28u%29%29+-+log%28%28v%29%29+-+4%2Alog%28%28z%29%29 ALIGN=MIDDLE  ALT=\"3%2Alog%28%28u%29%29+-+log%28%28v%29%29+-+4%2Alog%28%28z%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "There are 3 basic rules of logarithms.<BR>\n" );
document.write( "you will be using rules 2 and 3 as shown below.<BR>\n" );
document.write( "rule number 1 does not apply to this problem<BR>\n" );
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document.write( "rule number 1 states that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28a%2Ab%29%29+=+log%28%28a%29%29+%2B+log%28%28b%29%29 ALIGN=MIDDLE  ALT=\"log%28%28a%2Ab%29%29+=+log%28%28a%29%29+%2B+log%28%28b%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "rule number 2 states that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28a%2Fb%29%29+=+log%28%28a%29%29+-+log%28%28b%29%29 ALIGN=MIDDLE  ALT=\"log%28%28a%2Fb%29%29+=+log%28%28a%29%29+-+log%28%28b%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "rule number 3 states that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28a%5En%29%29+=+n%2Alog%28%28a%29%29 ALIGN=MIDDLE  ALT=\"log%28%28a%5En%29%29+=+n%2Alog%28%28a%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your equation of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Alog%28%28u%29%29+-+log%28%28v%29%29+-+4%2Alog%28%28z%29%29 ALIGN=MIDDLE  ALT=\"3%2Alog%28%28u%29%29+-+log%28%28v%29%29+-+4%2Alog%28%28z%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be first converted to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28u%5E3%29%29+-+log%28%28v%29%29+-+log%28%28z%5E4%29%29 ALIGN=MIDDLE  ALT=\"log%28%28u%5E3%29%29+-+log%28%28v%29%29+-+log%28%28z%5E4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > using rule number 3 in reverse.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your equation of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28u%5E3%29%29+-+log%28%28v%29%29+-+log%28%28z%5E4%29%29 ALIGN=MIDDLE  ALT=\"log%28%28u%5E3%29%29+-+log%28%28v%29%29+-+log%28%28z%5E4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be first converted to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28u%5E3%2Fv%29%29+-+log%28%28z%5E4%29%29 ALIGN=MIDDLE  ALT=\"log%28%28u%5E3%2Fv%29%29+-+log%28%28z%5E4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then converted to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28%28%28u%5E3%2Fv%29%29%2F%28z%5E4%29%29%29 ALIGN=MIDDLE  ALT=\"log%28%28%28%28u%5E3%2Fv%29%29%2F%28z%5E4%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > using rule number 2 in reverse if we apply the rule successively as we scan from left to right which we can do as long as there are no parentheses telling us to do otherwise.  Anything within parentheses is always done first.  That is not the case here since we have no parentheses in your original problem statement.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your final form is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28%28%28u%5E3%2Fv%29%29%2F%28z%5E4%29%29%29 ALIGN=MIDDLE  ALT=\"log%28%28%28%28u%5E3%2Fv%29%29%2F%28z%5E4%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to prove that this is true, we'll untangle it using the rules 1 and 2 of logarithms and we should be able to get back to the original equation.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your answer of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28%28%28u%5E3%2Fv%29%29%2F%28z%5E4%29%29%29 ALIGN=MIDDLE  ALT=\"log%28%28%28%28u%5E3%2Fv%29%29%2F%28z%5E4%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28u%5E3%2Fv%29+-+log%28%28z%5E4%29%29%29 ALIGN=MIDDLE  ALT=\"log%28%28u%5E3%2Fv%29+-+log%28%28z%5E4%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > using rule number 2<BR>\n" );
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document.write( "this becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28u%5E3%2Fv%29+-+4%2Alog%28%28z%29%29%29 ALIGN=MIDDLE  ALT=\"log%28%28u%5E3%2Fv%29+-+4%2Alog%28%28z%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > using rule number 3.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log%28%28u%5E3%29%29+-+log%28%28v%29%29%29+-+4%2Alog%28%28z%29%29%29 ALIGN=MIDDLE  ALT=\"%28log%28%28u%5E3%29%29+-+log%28%28v%29%29%29+-+4%2Alog%28%28z%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > using rule number 2.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Alog%28%28u%29%29+-+log%28%28v%29%29%29+-+4%2Alog%28%28z%29%29%29 ALIGN=MIDDLE  ALT=\"%283%2Alog%28%28u%29%29+-+log%28%28v%29%29%29+-+4%2Alog%28%28z%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > using rule number 3.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your original problem stated as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Alog%28%28u%29%29+-+log%28%28v%29%29+-+4%2Alog%28%28z%29%29%29 ALIGN=MIDDLE  ALT=\"3%2Alog%28%28u%29%29+-+log%28%28v%29%29+-+4%2Alog%28%28z%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is equivalent to my final version of your original problem as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Alog%28%28u%29%29+-+log%28%28v%29%29%29+-+4%2Alog%28%28z%29%29%29 ALIGN=MIDDLE  ALT=\"%283%2Alog%28%28u%29%29+-+log%28%28v%29%29%29+-+4%2Alog%28%28z%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > because my parentheses, in this case, do not alter the order of the operations to be performed.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );