document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1146418>Question 1146418</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me evaluate log27 base 3 + log6 base 3 - log54 base 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #767667 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=767667\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your problem is:\r<BR>\n" );
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document.write( "log3(27) + log3(6) - log3(54)\r<BR>\n" );
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document.write( "the rules of logarithms state that log(a*b/c) = log(a) + log(b) - log(c).\r<BR>\n" );
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document.write( "this rule applies regardless of the base of the logarithm as long as all the bases are the same.\r<BR>\n" );
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document.write( "this is the case in your problem.\r<BR>\n" );
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document.write( "also, the logarithms base conversion rule states that loga(x) = logb(x)/logb(a)\r<BR>\n" );
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document.write( "loga(x) means log(x) base a, as you have shown in your statement of the problem.\r<BR>\n" );
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document.write( "the log conversion rule is especially useful when using your calculator to find the log of any log to the base other than 10 (log function) or base other than e (ln function).\r<BR>\n" );
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document.write( "therefore, your problem can be solved as follows.\r<BR>\n" );
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document.write( "log3(27) + log3(6) - log3(54) = log3(27*6/54) = log10(27*6/54)/log10(3) = log(27*6/54)/log(3) using the log function of your calculator.\r<BR>\n" );
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document.write( "you could also have used the ln function of your calculator and gotten the same answer as shown below.\r<BR>\n" );
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document.write( "you would get:\r<BR>\n" );
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document.write( "log(27*6/54)/log(3) = 1\r<BR>\n" );
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document.write( "ln(27*6/54)/ln(3) = 1\r<BR>\n" );
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document.write( "you could also have converted to base 10 before anything else as shown below:\r<BR>\n" );
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document.write( "log3(27) + log3(6) - log3(54) = log(27)/log(3) + log(6)/log(3) - log54)/log(3) = (log(27) + log(6) - log(54)) / log(3).\r<BR>\n" );
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document.write( "at this point, you could have just used your calculator to get (log(27) + log(6) - log(54)) / log(3) = 1, or you could have converted using the rules of logarithms to get log(27 * 6 / 54) / log(3) = 1.\r<BR>\n" );
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document.write( "using log function without specifying the base implies log10.<BR>\n" );
document.write( "this is the default for all calculator log functions that i know of.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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