document.write( "Question 354490: Expand as much as possible into individual logarithms:\r
\n" ); document.write( "\n" ); document.write( "log2 {(sqrt(x)(x-5))/y^3}\r
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\n" ); document.write( "\n" ); document.write( "Thank you for your help! I appreciate that!
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Algebra.Com's Answer #253326 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"log%282%2C+%28%28sqrt%28x%29%28x-5%29%29%2Fy%5E3%29%29\"$
\n" ); document.write( "We can start by using a property of logarithms, $\"log%28a%2C+%28p%2Fq%29%29+=+log%28a%2C+%28p%29%29+-+log%28a%2C+%28q%29%29\"$ , to split the log of a fraction into separate logs:
\n" ); document.write( " $\"log%282%2C+%28sqrt%28x%29%28x-5%29%29%29+-+log%282%2C+%28y%5E3%29%29\"$
\n" ); document.write( "Next, on the first log, we can use another property of logarithms, $\"log%28a%2C+%28p%2Aq%29%29+=+log%28a%2C+%28p%29%29+%2B+log%28a%2C+%28q%29%29\"$ , to separate the log of a product into separate logs:
\n" ); document.write( " $\"log%282%2C+%28sqrt%28x%29%29%29+%2B+log%282%2C+%28x-5%29%29+-+log%282%2C+%28y%5E3%29%29\"$
\n" ); document.write( "This is as many logs as we can get. But often these problems want you to use yet a third property of logarithms, $\"log%28a%2C+%28p%5Eq%29%29+=+q%2Alog%28a%2C+%28p%29%29\"$ , to remove exponents. But first, we will rewrite the square root using a fractional exponent:
\n" ); document.write( " $\"log%282%2C+%28x%5E%281%2F2%29%29%29+%2B+log%282%2C+%28x-5%29%29+-+log%282%2C+%28y%5E3%29%29\"$
\n" ); document.write( "Now we will use the property on the first and last logs to move their exponents out in front:
\n" ); document.write( " $\"%281%2F2%29log%282%2C+%28x%29%29+%2B+log%282%2C+%28x-5%29%29+-+3%2Alog%282%2C+%28y%29%29\"$ \n" ); document.write( "

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