document.write( "Question 812884: Use the properties of logarithms to write the expression in terms of the logarithms of x, y, and z. logb ( x^3y^2 z^4)^(1/4)
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Algebra.Com's Answer #489398 by jsmallt9(3758) $\"\"$ $\"About$

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$\"log%28b%2C+%28%28x%5E3+%2A+y%5E2+%2A+z%5E4%29%5E%281%2F4%29%29%29\"$
\n" ); document.write( "There are three properties of logarithms that are often used in problems like this:

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

Since the argument of our log contains just products and powers we will be using just the first and last properties.

\n" ); document.write( "First we will use the last property which allows us to move the exponent of the argument out in front:
\n" ); document.write( " $\"%281%2F4%29%2Alog%28b%2C+%28x%5E3+%2A+y%5E2+%2A+z%5E4%29%29\"$
\n" ); document.write( "The argument is now a product. So we will use the first property to split the log of the product into the sum of the logs of the factors:
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\n" ); document.write( "Note the parentheses around the logs. It is a good habit to put parentheses around a substitution, especially if there are more terms. The arguments of the three logs are all powers. So we will use the last property again to move the exponents out in front:
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\n" ); document.write( "Since the expression is now in terms of logs of x, y and z we might be done. But we should probably use the Distributive Property to multiply out the 1/4:
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