document.write( "Question 883007: how to expand ln x^3(x-2)^2/ sqrt x^2+5 \n" ); document.write( "

Algebra.Com's Answer #533246 by Leaf W.(135) $\"\"$ $\"About$

You can put this solution on YOUR website!
Hello!
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\n" ); document.write( "You can use a few \"logarithm rules\" to expand out logarithms of any base:
\n" ); document.write( "1. The log of the product of two numbers is the same as adding the individual logs of each number: $\"log+%28a%2C+%28bc%29%29+=+log+%28a%2C+b%29+%2B+log+%28a%2C+c%29\"$
\n" ); document.write( "2. The log of the quotient of two numbers is the same as subtracting the individual logs of each number: $\"log%28a%2C%28b%2Fc%29%29+=+log%28a%2Cb%29+-+log%28a%2Cc%29\"$
\n" ); document.write( "3. The log of a number raised to a certain exponent is the same as the value of that exponent multiplied by the log of that number: $\"log%28a%2C%28b%5Ec%29%29+=+c%2Alog%28a%2Cb%29\"$
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\n" ); document.write( "Now let us apply those rules to this case!
\n" ); document.write( " $\"ln%28%28x%5E3+%2A+%28x+-+2%29%5E2%29%2F%28sqrt%28x%5E2%2B5%29%29%29\"$
\n" ); document.write( "Use rule #2 to get rid of the division: $\"ln%28x%5E3+%2A+%28x-2%29%5E2%29+-+ln%28sqrt%28x%5E2+%2B+5%29%29\"$
\n" ); document.write( "Use rule #1 to get rid of the multiplication: $\"ln%28x%5E3%29+%2B+ln%28%28x-2%29%5E2%29+-+ln%28sqrt%28x%5E2+%2B+5%29%29\"$
\n" ); document.write( "Since taking the square root is the same thing as raising to the one-half power: $\"ln%28x%5E3%29+%2B+ln%28%28x+-+2%29%5E2%29+-+ln%28%28x%5E2+%2B+5%29%5E%281%2F2%29%29\"$
\n" ); document.write( "Use rule #3 to get rid of exponents: $\"3ln%28x%29+%2B+2ln%28x+-+2%29+-+%281%2F2%29ln%28x%5E2+%2B+5%29\"$
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\n" ); document.write( "Therefore, the expanded expression is $\"3ln%28x%29+%2B+2ln%28x+-+2%29+-+%281%2F2%29ln%28x%5E2+%2B+5%29\"$
\n" ); document.write( "I hope this helps! =) \n" ); document.write( "

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