document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159162>Question 159162</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Explain the difference between a logarithm of a product and the product of logarithm. Please give examples </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117320 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=117320\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> log of (a*b) = log(a) + log(b)<BR>\n" );
document.write( "log(a) * log(b) is simply the product of the 2 logarithms.<BR>\n" );
document.write( "----------------------------------------------<BR>\n" );
document.write( "an example of log of (a*b) is:<BR>\n" );
document.write( "let a = 5<BR>\n" );
document.write( "let b = 7<BR>\n" );
document.write( "then log (5*7) = log(35) = 1.544.....<BR>\n" );
document.write( "log (5) + log (7) = 1.544.....<BR>\n" );
document.write( "they log (5) + log(7) = log (7*5) = log(35)<BR>\n" );
document.write( "--------------------------------------------------------<BR>\n" );
document.write( "an example of the multiplication of 2 logarithms is a property of logarithms where logarithms of any base are proportional to each other.<BR>\n" );
document.write( "this means that log(7)/log(5) = ln(7)/ln(5) = log of 7 to the base 3 / log of 5 to the base 3.<BR>\n" );
document.write( "i'll use the first 2 because the calculator does those automatically.<BR>\n" );
document.write( "log(7)/log(5) = 1.20906.....<BR>\n" );
document.write( "ln(7)/ln(5) = 1.20906......<BR>\n" );
document.write( "the ratio holds.<BR>\n" );
document.write( "if the ratio holds then log(7)*ln(5) = log(5)*ln(7)<BR>\n" );
document.write( "1.36013.... = 1.36013.....<BR>\n" );
document.write( "they are equal to each other.<BR>\n" );
document.write( "-----------------------------------------------------------<BR>\n" );
document.write( "an example where logarithms are divided is the base conversion formula<BR>\n" );
document.write( "where log of x to the base b = log of x to the base c / log of b to the base c.<BR>\n" );
document.write( "if i want to convert from ln of a number to log of that number to the base 10 i would follow the formula as follows:<BR>\n" );
document.write( "let my number = 722.<BR>\n" );
document.write( "ln (722) = 6.582025139<BR>\n" );
document.write( "if i wanted to convert that to the base 10, i would take log (722) / log(e)<BR>\n" );
document.write( "log (722) = 2.858537198<BR>\n" );
document.write( "log (e) = .434294482<BR>\n" );
document.write( "log (722) / log (e) = 2.858537198/.434294482 = 6.582025139.<BR>\n" );
document.write( "---------------------------------------------------------------<BR>\n" );
document.write( "log (a/b) = log (a) - log (b)<BR>\n" );
document.write( "log(a)/log(b) is just a division<BR>\n" );
document.write( "--------------------------------------------------------<BR>\n" );
document.write( "i didn't see in the literature where log(a)*log(b) and log(a)/log(b) was used for other than a straight multiplication or division.<BR>\n" );
document.write( "---------------------------------------<BR>\n" );
document.write( "caveat:<BR>\n" );
document.write( "from what i researched, i believe this is accurate but i would caution you to confirm with other sources before accepting this as gospel.<BR>\n" );
document.write( "i didn't see any other application for log(a)*log(b) or log(a)/log(b) which doesn't mean there isn't any.  it just means i didn't see it.  it's definitely not one of the basic operations of logarithms because it's not listed as one of them.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );