document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30180>Question 30180</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the expression as a single natural logarithm.<BR>\n" );
document.write( "ln a-2 ln b+1/2 ln c<BR>\n" );
document.write( "Thanks for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #16880 by </B><A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><B>sdmmadam@yahoo.com(530)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><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=16880\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write the expression as a single natural logarithm.<BR>\n" );
document.write( "ln a-2 ln b+1/2 ln c<BR>\n" );
document.write( "Thanks for your help\r<BR>\n" );
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document.write( "(ln a)- 2(ln b)+1/2 (ln c)<BR>\n" );
document.write( "=log(a)-log(b^2)+log[c^(1/2)]  ( using n[log m)]= log(m^n))<BR>\n" );
document.write( "=log(a)+log[c^(1/2)]-log(b^2) <BR>\n" );
document.write( "(by additive commutativity (second and third terms)  <BR>\n" );
document.write( "= {log(a)+log[c^(1/2)]}-log(b^2)  (by additive associativity)<BR>\n" );
document.write( "=log{a[c^(1/2)]}-log(b^2)  (using sum of logarithms = log of product)<BR>\n" );
document.write( "=log{a[c^(1/2)]/(b^2)} to the base e of course as we are talking about natural logarithms.<BR>\n" );
document.write( "Answer:log[a(c^(1/2))/b^2]<BR>\n" );
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