document.write( "Question 288337: express as a sums/difference log17 (x^3y^5/z^4) I goofed on the previous question posted. \n" ); document.write( "

Algebra.Com's Answer #209139 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
The reference to \"sums/differences\" should bring to mind two of the properties of logarithms:

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

\n" ); document.write( " $\"log%2817%2C+%28x%5E3y%5E5%2Fz%5E4%29%29\"$
\n" ); document.write( "We can start by using the second property, because of the division:
\n" ); document.write( " $\"log%2817%2C+%28x%5E3y%5E5%29%29+-+log%2817%2C+%28z%5E4%29%29\"$
\n" ); document.write( "And now the first property because of the multiplication:
\n" ); document.write( " $\"log%2817%2C+%28x%5E3%29%29+%2B+log%2817%2C+%28y%5E5%29%29+-+log%2817%2C+%28z%5E4%29%29\"$
\n" ); document.write( "This may the the desired answer. Or you could use a third property, $\"log%28a%2C+%28p%5Eq%29%29+=+q%2Alog%28a%2C+%28p%29%29\"$ , to move the exponents out in front:
\n" ); document.write( " $\"3log%2817%2C+%28x%29%29+%2B+5log%2817%2C+%28y%29%29+-+4log%2817%2C+%28z%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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