document.write( "Question 376797: Write Logb(that is base b)x^3y^2/z(that is a fraction) in terms of the logarithms of x, y, and z. \n" ); document.write( "

Algebra.Com's Answer #268023 by jsmallt9(3758) $\"\"$ $\"About$

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$\"log%28b%2C+%28x%5E3y%5E2%2Fz%29%29\"$
\n" ); document.write( "There are three properties of logarithms which can be used to manipulate arguments of logarithms:

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

\n" ); document.write( "Since your argument is a fraction/division, we willstart by using the second property to split the numerator and denominator into their own logarithms:
\n" ); document.write( " $\"log%28b%2C+%28x%5E3y%5E2%29%29+-+log%28b%2C+%28z%29%29\"$
\n" ); document.write( "Next we can use the first property on the first logarithm, since its argument is a product:
\n" ); document.write( " $\"log%28b%2C+%28x%5E3%29%29+%2B+log%28b%2C+%28y%5E2%29%29+-+log%28b%2C+%28z%29%29\"$
\n" ); document.write( "And last we can use the third property on the first two logarithms, since their arguments have exponents:
\n" ); document.write( " $\"3%2Alog%28b%2C+%28x%29%29+%2B+2%2Alog%28b%2C+%28y%29%29+-+log%28b%2C+%28z%29%29\"$
\n" ); document.write( "This expression is equivalent to the original expression and it it expressed in terms of the base b logarithms of x, y and z. \n" ); document.write( "

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