document.write( "Question 1201530: I have to simplify the following - all base 10 logarithms:\r
\n" ); document.write( "\n" ); document.write( "log(a)-1/2log(4a)\r
\n" ); document.write( "\n" ); document.write( "I get this far:\r
\n" ); document.write( "\n" ); document.write( "log(a) - log(4a)^1/2\r
\n" ); document.write( "\n" ); document.write( "log[a/(4a)^1/2]\r
\n" ); document.write( "\n" ); document.write( "but then I get stuck! \n" ); document.write( "

Algebra.Com's Answer #852270 by ikleyn(52915) $\"\"$ $\"About$

You can put this solution on YOUR website!
I have to simplify the following - all base 10 logarithms:
\n" ); document.write( "log(a)-1/2log(4a)
\n" ); document.write( "I get this far:
\n" ); document.write( "log(a) - log(4a)^1/2
\n" ); document.write( "log[a/(4a)^1/2]
\n" ); document.write( "but then I get stuck!
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document.write( "Using the standard rules of logarithms, solve it this way\r\n" );
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document.write( "      log(a) - (1/2)*log(4a) = log(a) - (1/2) * [log(4) + log(a)] = log(a) - (1/2)*log(4) - (1/2)*log(a)  (*)\r\n" );
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document.write( "Combine the 1st and the 3rd terms in (*)  log(a) - (1/2)*log(a) = (1/2)*log(a).\r\n" );
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document.write( "Transform the 2nd term in (*)              (1/2)*log(4) = (1/2) * (2*log(2)) = log(2).\r\n" );
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document.write( "So, you can continue line (*) in this way\r\n" );
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document.write( "       log(a) - (1/2)*log(4a) = (1/2)*log(a) - log(2).   (1)\r\n" );
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document.write( "The rest depends for whom you do this assignment.\r\n" );
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document.write( "If it is a Math assignment, then you transform right side of (1) into  \r\n" );
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document.write( "        log(a) - (1/2)*log(4a) = .\r\n" );
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document.write( "It gives you the answer in simplest mathematical form.\r\n" );
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document.write( "If you simplify for  \"Computer Science\",  they prefer another form as a \"simplest\"\r\n" );
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document.write( "    log(a) - (1/2)*log(4a) = (1/2)*log(a) - log(2),    (2)\r\n" );
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document.write( "same as (1).\r\n" );
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document.write( "Why ? - - - because, firstly, then we do not need calculate ,\r\n" );
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document.write( "                and, secondly, log(2) can be considered as a constant.\r\n" );
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document.write( "So, if there is the need to compute log(a) - (1/2)*log(4a)  many times for different values of 'a'\r\n" );
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document.write( "(as it often happens in computing),  then form (2) is preferable. \r\n" );
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document.write( "For computing, they do not use the term \"simplest form\" of an expression.\r\n" );
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document.write( "Instead, they think about the form, which is most    for calculations,\r\n" );
document.write( "i.e. requires minimum of arithmetic operations.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, with explanations.\r
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