document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113487>Question 113487</A>: <I><SPAN STYLE=\"word-break: break-all;\"> simplify log1 -3 log2 + log16 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82551 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=82551\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First recognize that log(1) = 0. [This is true regardless of what base logarithm is used.]<BR>\n" );
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document.write( "Next, work on -3*log(2). By the rules of logarithms, the multiplier of a logarithm (in this<BR>\n" );
document.write( "case that multiplier is -3) can become the exponent of the quantity that the log is operating<BR>\n" );
document.write( "on. That is to say -3*log(2) is equivalent to log(2^(-3)). But 2^(-3) equals 1/(2^3) by<BR>\n" );
document.write( "the rules of exponents. And 1/(2^3) = 1/8 when you cube 2. Therefore, -3*log(2) converts to<BR>\n" );
document.write( "log(1/8).<BR>\n" );
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document.write( "At this point the original problem has been converted to:<BR>\n" );
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document.write( "0 + log(1/8) + log(16)<BR>\n" );
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document.write( "and the zero can be dropped so that the problem is just:<BR>\n" );
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document.write( "log(1/8) + log(16)<BR>\n" );
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document.write( "Recognize now that by the rules of logarithms the sum of two logarithms is equal to the<BR>\n" );
document.write( "log of their product. Applying this rule to the problem results in:<BR>\n" );
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document.write( "log(1/8) + log(16) = log((1/8)*16) = log(16/8) = log(2)<BR>\n" );
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document.write( "The answer to the problem is log(2) <BR>\n" );
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document.write( "You can check this answer by using a scientific calculator as follows:<BR>\n" );
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document.write( "a) Return to the original problem. Use the calculator to find log of 1. You should get zero<BR>\n" );
document.write( "as the answer to that part of the problem.<BR>\n" );
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document.write( "b) Use the calculator to find the base 10 log of 2. The answer to that should be 0.301029995. <BR>\n" );
document.write( "Multiply that by -3 and you should have -0.903089987<BR>\n" );
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document.write( "c) Use the calculator to find the base 10 log of 16. You should get 1.204119983<BR>\n" );
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document.write( "d) Total all the results ... 0 - 0.903089987 + 1.20411983 = 0.301029995<BR>\n" );
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document.write( "That's the result of working the problem. But we found that log(2) should be equivalent<BR>\n" );
document.write( "to that. So use the calculator to find the base 10 log of 2 and you will see that it<BR>\n" );
document.write( "indeed is 0.301029995 ... which verifies that log(2) is equivalent to the original problem.<BR>\n" );
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document.write( "Hope this helps you to see your way through this problem and to understand the rules of<BR>\n" );
document.write( "logarithms and exponents a little better.<BR>\n" );
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