document.write( "Question 368653: Write the expression in terms of simpler logarithmic forms. \r
\n" ); document.write( "\n" ); document.write( "ln x^4y^2/z^1/2 \n" ); document.write( "

Algebra.Com's Answer #262877 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"ln%28%28x%5E4y%5E2%29%2Fz%5E%281%2F2%29%29\"$
\n" ); document.write( "There are three properties of logarithms which can be used to manipulate them:

$\"log%28a%2C+%28p%2Aq%29%29+=+log%28a%2C+%28p%29%29+%2B+log%28a%2C+%28q%29%29\"$
$\"log%28a%2C+%28p%2Fq%29%29+=+log%28a%2C+%28p%29%29+-+log%28a%2C+%28q%29%29\"$
$\"log%28a%2C+%28p%5Eq%29%29+=+q%2Alog%28a%2C+%28p%29%29\"$

\n" ); document.write( "Since the argument of your logarithm is a division/fraction, we will use the second property to split it into two logarithms:
\n" ); document.write( " $\"ln%28x%5E4y%5E2%29+-+ln%28z%5E%281%2F2%29%29\"$
\n" ); document.write( "The argument of the first logarithm is a product so we will use the first property to split it into two logarithms:
\n" ); document.write( " $\"ln%28x%5E4%29+%2B+ln%28y%5E2%29+-+ln%28z%5E%281%2F2%29%29\"$
\n" ); document.write( "The arguments all three logarithms have an exponent. We can use the third property on them to move the argument out in front:
\n" ); document.write( " $\"4%2Aln%28x%29+%2B+2%2Aln%28y%29+-+%281%2F2%29%2Aln%28z%29\"$
\n" ); document.write( "By using the properties as we have, the expression as a whole is more complex but the arguments of the logarithms are now just a simple variable. \n" ); document.write( "

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