document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200720>Question 1200720</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ln12 - ln4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834919 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=834919\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ln(12) - ln(4) = ln(12/4) = ln(3) = 1.098612289.<BR>\n" );
document.write( "confirm by using your calculator in the original format and the converted format.<BR>\n" );
document.write( "ln(12) - ln(4) = the same.<BR>\n" );
document.write( "ln(12/4) = the same.<BR>\n" );
document.write( "you can also do e^1.098612289 = 3.<BR>\n" );
document.write( "that's because e^x = y if and only if ln(y) = x<BR>\n" );
document.write( "in this case, x = 1.098612289 and y = 3.<BR>\n" );
document.write( "hee's some log rules that should help you to understand.<BR>\n" );
document.write( "your problem, however, didn't need any conversion, since it could be analyzed as it was presented by a calculator that can do natural logs.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://mathinsight.org/logarithm_basics\" target = \"_blank\">https://mathinsight.org/logarithm_basics</a><BR>\n" );
document.write( "let me know if you have any further questions.<BR>\n" );
document.write( "theo </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );