document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199481>Question 1199481</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If x^2+y^2=146xy then show that 2*log(x-y)=4*log2+2*log3+logx+logy </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833391 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=833391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Let's start with the equation<BR>\n" );
document.write( "2*log(x-y) = 4*log(2)+2*log(3)+log(x)+log(y)<BR>\n" );
document.write( "and use log rules to say the following shown below.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2*log(x-y) = 4*log(2)+2*log(3)+log(x)+log(y)<BR>\n" );
document.write( "log( (x-y)^2 ) = log(2^4)+log(3^2)+log(x)+log(y)<BR>\n" );
document.write( "log( (x-y)^2 ) = log(16)+log(9)+log(x)+log(y)<BR>\n" );
document.write( "log( (x-y)^2 ) = log(16*9*x*y)<BR>\n" );
document.write( "log( (x-y)^2 ) = log(144xy)<BR>\n" );
document.write( "(x-y)^2 = 144xy\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then expand out the left side and do a bit of moving terms around<BR>\n" );
document.write( "(x-y)^2 = 144xy<BR>\n" );
document.write( "x^2-2xy+y^2 = 144xy<BR>\n" );
document.write( "x^2+y^2 = 144xy+2xy<BR>\n" );
document.write( "x^2+y^2 = 146xy\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We started with <BR>\n" );
document.write( "2*log(x-y) = 4*log(2)+2*log(3)+log(x)+log(y)<BR>\n" );
document.write( "and ended with <BR>\n" );
document.write( "x^2+y^2 = 146xy\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That process can be done in reverse to go from <BR>\n" );
document.write( "x^2+y^2 = 146xy<BR>\n" );
document.write( "to <BR>\n" );
document.write( "2*log(x-y) = 4*log(2)+2*log(3)+log(x)+log(y)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The steps would look like this<BR>\n" );
document.write( "x^2+y^2 = 146xy<BR>\n" );
document.write( "x^2+y^2 = 144xy+2xy<BR>\n" );
document.write( "x^2-2xy+y^2 = 144xy<BR>\n" );
document.write( "(x-y)^2 = 144xy<BR>\n" );
document.write( "log( (x-y)^2 ) = log(144xy)<BR>\n" );
document.write( "log( (x-y)^2 ) = log(16*9*x*y)<BR>\n" );
document.write( "log( (x-y)^2 ) = log(16)+log(9)+log(x)+log(y)<BR>\n" );
document.write( "log( (x-y)^2 ) = log(2^4)+log(3^2)+log(x)+log(y)<BR>\n" );
document.write( "2*log(x-y) = 4*log(2)+2*log(3)+log(x)+log(y)<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );