document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149932>Question 149932</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4[ln(z)+ln(z+5)]-2ln(z-50<BR>\n" );
document.write( "i need to condense this to a single quantity.  This is as far as I get.<BR>\n" );
document.write( "[ln(z)+ln(z+5)]^4 - ln(z-5)^2  now can I pull another 2 out as a multiplier?like this:    2(ln(z+5))^4 - ln(z-5)^2  NOW I AM STUCK </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #110035 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=110035\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 4\left\[\ln(z)+\ln(z+5)\right\]-2\ln(z-5)\"> Start with the given expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 4\ln(z)+4\ln(z+5)-2\ln(z-5)\"> Distribute.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ln(z^4)+\ln\left((z+5)^4\right)-\ln\left((z-5)^2\right)\"> Rewrite each term using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%5Ey%29=y%2Aln%28x%29%29 ALIGN=MIDDLE  ALT=\"ln%28x%5Ey%29=y%2Aln%28x%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/rendertex.cgi?\LARGE \ln\left(z^4(z+5)^4\right)-\ln\left((z-5)^2\right)\"> 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/rendertex.cgi?\LARGE \ln\left(\frac{z^4(z+5)^4}{(z-5)^2}\right)\"> Combine the 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( "So <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 4\left\[\ln(z)+\ln(z+5)\right\]-2\ln(z-5)\"> simplifies to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ln\left(\frac{z^4(z+5)^4}{(z-5)^2}\right)\"> </SPAN>\n" );
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