document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1099475>Question 1099475</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Expand as the sum of individual logarithms, each of whose argument is linear. Simplify your answer. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28%28x%2B1%29%5E3%29+%28sqrt%28y%29%29%29%2F%28sqrt%28y%2B3%29%28x%2B1%29%5E2%29+ ALIGN=MIDDLE  ALT=\"+%28%28%28x%2B1%29%5E3%29+%28sqrt%28y%29%29%29%2F%28sqrt%28y%2B3%29%28x%2B1%29%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-Accidentally submitted this question before I was done writing it, so that's why there's a second question like this one.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #713918 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13215)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=713918\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>By the laws of exponents, and therefore by the laws of logarithms, when you take logarithms, all exponents come out in front as multipliers of the logarithms.<br><BR>\n" );
document.write( "And roots are fractional powers; in this example, each square root is a one-half power.<br><BR>\n" );
document.write( "And then of course you need to use the rules that say multiplying means adding logarithms and dividing means subtracting logarithms.<br><BR>\n" );
document.write( "Put that all together and we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Alog%28%28x%2B1%29%29%2B%281%2F2%29%2Alog%28y%29-%281%2F2%29log%28%28y%2B3%29%29-2%2Alog%28%28x%2B1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "There are two terms with log(x+1) which can be combined:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28x%2B1%29%29%2B%281%2F2%29log%28y%29-%281%2F2%29log%28%28y%2B3%29%29 ALIGN=MIDDLE  ALT=\"log%28%28x%2B1%29%29%2B%281%2F2%29log%28y%29-%281%2F2%29log%28%28y%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,br><BR>\n" );
document.write( "Of course, there was also the option to do the simplification before taking the logarithm.... </SPAN>\n" );
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