document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=208979>Question 208979</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780471793038/algebrahomeworkh>functions modelling change</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> i need help to simplify fully this logarithm expression, please...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28A%2BB%29-ln%28A%5E-1%2BB%5E-1%29 ALIGN=MIDDLE  ALT=\"ln%28A%2BB%29-ln%28A%5E-1%2BB%5E-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "thank you!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157990 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=157990\">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=ln%28A%2BB%29-ln%28A%5E-1%2BB%5E-1%29 ALIGN=MIDDLE  ALT=\"ln%28A%2BB%29-ln%28A%5E-1%2BB%5E-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "by the laws of logarithms,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%29+-+ln%28y%29+=+ln%28x%2Fy%29 ALIGN=MIDDLE  ALT=\"ln%28x%29+-+ln%28y%29+=+ln%28x%2Fy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if you let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+A%2BB ALIGN=MIDDLE  ALT=\"x+=+A%2BB\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+A%5E-1+%2B+B%5E-1 ALIGN=MIDDLE  ALT=\"y+=+A%5E-1+%2B+B%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then your equation becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28%28A%2BB%29%2F%28A%5E-1%2BB%5E-1%29%29 ALIGN=MIDDLE  ALT=\"ln%28%28A%2BB%29%2F%28A%5E-1%2BB%5E-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your denominator of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A%5E-1%2BB%5E-1%29 ALIGN=MIDDLE  ALT=\"%28A%5E-1%2BB%5E-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2FA%29+%2B+%281%2FB%29 ALIGN=MIDDLE  ALT=\"%281%2FA%29+%2B+%281%2FB%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28A%2BB%29%2F%28BA%29%29 ALIGN=MIDDLE  ALT=\"%28%28A%2BB%29%2F%28BA%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > once you multiply the first term by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%2FB ALIGN=MIDDLE  ALT=\"B%2FB\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the second term by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2FA ALIGN=MIDDLE  ALT=\"A%2FA\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your equation becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28%28A%2BB%29%2F%28%28A%2BB%29%2F%28BA%29%29%29 ALIGN=MIDDLE  ALT=\"ln%28%28A%2BB%29%2F%28%28A%2BB%29%2F%28BA%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this is the same as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28%28%28A%2BB%29%2A%28BA%29%29%2F%28A%2BB%29%29 ALIGN=MIDDLE  ALT=\"ln%28%28%28A%2BB%29%2A%28BA%29%29%2F%28A%2BB%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28BA%29 ALIGN=MIDDLE  ALT=\"ln%28BA%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this can then be further simplified to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28A%29+%2B+ln%28B%29 ALIGN=MIDDLE  ALT=\"ln%28A%29+%2B+ln%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to prove correct, substitute for A + B in the original equation and then see if you can solve the original equation and the simplified equation and get the same answer.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let A = 8 and let B = 15<BR>\n" );
document.write( "original equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28A%2BB%29-ln%28A%5E-1%2BB%5E-1%29 ALIGN=MIDDLE  ALT=\"ln%28A%2BB%29-ln%28A%5E-1%2BB%5E-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%288%2B15%29-ln%28%288%29%5E-1%2B%2815%29%5E-1%29 ALIGN=MIDDLE  ALT=\"ln%288%2B15%29-ln%28%288%29%5E-1%2B%2815%29%5E-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4.787491743<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "simplified equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28A%29+%2B+ln%28B%29 ALIGN=MIDDLE  ALT=\"ln%28A%29+%2B+ln%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%288%29+%2B+ln%2815%29 ALIGN=MIDDLE  ALT=\"ln%288%29+%2B+ln%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4.787491743<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "these are both equivalent since they are equal to the same number.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );