document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=211992>Question 211992</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Express as a single logarithm, simplify if possible<BR>\n" );
document.write( "log(w)(x^2-64)-log(w)(x-8) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #161475 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=161475\">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=log%28w%2C%28x%5E2-64%29%29-log%28w%2C%28x-8%29%29 ALIGN=MIDDLE  ALT=\"log%28w%2C%28x%5E2-64%29%29-log%28w%2C%28x-8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "basic laws of logarithms<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "<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( "<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( "your problem looks like the second one.<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28w%2C%28x%5E2-64%29%29+-+log%28w%2C%28x-8%29%29 ALIGN=MIDDLE  ALT=\"log%28w%2C%28x%5E2-64%29%29+-+log%28w%2C%28x-8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28w%2C%28%28x%5E2-64%29%2F%28x-8%29%29%29 ALIGN=MIDDLE  ALT=\"log%28w%2C%28%28x%5E2-64%29%2F%28x-8%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-64%29%2F%28x-8%29+=+%28x-8%29%2A%28x%2B8%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-64%29%2F%28x-8%29+=+%28x-8%29%2A%28x%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B8%29 ALIGN=MIDDLE  ALT=\"%28x%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > so the logarithm formula becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28w%2C%28x%2B8%29%29 ALIGN=MIDDLE  ALT=\"log%28w%2C%28x%2B8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to confirm this is true, let w = 10, and let x = 20 and solve (any number for w and x would do but the base of 10 can be solved using the calculator and 20 is just a nice number easy to remember and use).  I also had to make sure that I was not taking the log of a negative number because that is not allowed.  20 is big enough so that doesn't happen).<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28w%2C%28x%5E2-64%29%29-log%28w%2C%28x-8%29%29 ALIGN=MIDDLE  ALT=\"log%28w%2C%28x%5E2-64%29%29-log%28w%2C%28x-8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%2820%5E2-64%29%29-log%2810%2C%2820-8%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%2820%5E2-64%29%29-log%2810%2C%2820-8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%28336%29%29-log%2810%2C%2812%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%28336%29%29-log%2810%2C%2812%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.447158031<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28w%2C%28x%2B8%29%29 ALIGN=MIDDLE  ALT=\"log%28w%2C%28x%2B8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%2820%2B8%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%2820%2B8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%2828%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%2828%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.447158031<BR>\n" );
document.write( "----<BR>\n" );
document.write( "the two equations are identical.<BR>\n" );
document.write( "----- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );