document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=322465>Question 322465</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please combine 4 ln sqrt x - ln (xy^5) + 3 ln y?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #230841 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=230841\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4ln%28sqrt%28x%29%29-ln%28xy%5E5%29%2B3ln%28y%29 ALIGN=MIDDLE  ALT=\"4ln%28sqrt%28x%29%29-ln%28xy%5E5%29%2B3ln%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4ln%28x%5E%281%2F2%29%5E%22%22%29-ln%28xy%5E5%29%2B3ln%28y%29 ALIGN=MIDDLE  ALT=\"4ln%28x%5E%281%2F2%29%5E%22%22%29-ln%28xy%5E5%29%2B3ln%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Convert to exponential notation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%5E%284%281%2F2%29%29%5E%22%22%29-ln%28xy%5E5%29%2Bln%28y%5E3%29 ALIGN=MIDDLE  ALT=\"ln%28x%5E%284%281%2F2%29%29%5E%22%22%29-ln%28xy%5E5%29%2Bln%28y%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Aln%28x%29=ln%28x%5Ey%29 ALIGN=MIDDLE  ALT=\"y%2Aln%28x%29=ln%28x%5Ey%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=ln%28x%5E%284%2F2%29%5E%22%22%29-ln%28xy%5E5%29%2Bln%28y%5E3%29 ALIGN=MIDDLE  ALT=\"ln%28x%5E%284%2F2%29%5E%22%22%29-ln%28xy%5E5%29%2Bln%28y%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%5E2%29-ln%28xy%5E5%29%2Bln%28y%5E3%29 ALIGN=MIDDLE  ALT=\"ln%28x%5E2%29-ln%28xy%5E5%29%2Bln%28y%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28%28x%5E2%29%2F%28xy%5E5%29%29%2Bln%28y%5E3%29 ALIGN=MIDDLE  ALT=\"ln%28%28x%5E2%29%2F%28xy%5E5%29%29%2Bln%28y%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the first two logs using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28A%29-ln%28B%29=ln%28A%2FB%29 ALIGN=MIDDLE  ALT=\"ln%28A%29-ln%28B%29=ln%28A%2FB%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=ln%28%28%28x%5E2%29%2F%28xy%5E5%29%29%28y%5E3%29%29 ALIGN=MIDDLE  ALT=\"ln%28%28%28x%5E2%29%2F%28xy%5E5%29%29%28y%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the logs using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28A%29%2Bln%28B%29=ln%28A%2AB%29 ALIGN=MIDDLE  ALT=\"ln%28A%29%2Bln%28B%29=ln%28A%2AB%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=ln%28%28x%5E2y%5E3%29%2F%28xy%5E5%29%29 ALIGN=MIDDLE  ALT=\"ln%28%28x%5E2y%5E3%29%2F%28xy%5E5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%2F%28y%5E2%29%29 ALIGN=MIDDLE  ALT=\"ln%28x%2F%28y%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4ln%28sqrt%28x%29%29-ln%28xy%5E5%29%2B3ln%28y%29=ln%28x%2F%28y%5E2%29%29 ALIGN=MIDDLE  ALT=\"4ln%28sqrt%28x%29%29-ln%28xy%5E5%29%2B3ln%28y%29=ln%28x%2F%28y%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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