document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=31386>Question 31386</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation:  \r<BR>\n" );
document.write( "\n" );
document.write( "log(3+x)-log(x-3)=log 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18083 by </B><A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><B>mukhopadhyay(490)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><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=18083\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> log(3+x)-log(x-3)=log 3<BR>\n" );
document.write( "=>log[(x+3)(x-3)]=log 3<BR>\n" );
document.write( "=>log (x^2-9)=log 3<BR>\n" );
document.write( "=>x^2-9 = 3<BR>\n" );
document.write( "=>x^2 = 12<BR>\n" );
document.write( "=>x = sqrt(12) or x = -sqrt(12) <BR>\n" );
document.write( "x cannot be anyone of them because log(x-3) and log(x+3) are valid as long as (x-3) is not negative and (x+3) is not negative. \r<BR>\n" );
document.write( "\n" );
document.write( "(x-3) is negative if x = sqrt(12) or x = -sqrt(12)\r<BR>\n" );
document.write( "\n" );
document.write( "So, the answer is x has a null set \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );