document.write( "Question 33712: Express as a single logarithm and, if possible simplify
\n" ); document.write( "log(x^3-8)-log(x-2) \n" ); document.write( "

Algebra.Com's Answer #20118 by ntnk(54) $\"\"$ $\"About$

You can put this solution on YOUR website!
First, note that when factoring a binomial in the form: $\"a%5E3+-+b%5E3\"$ , it is simplified as $\"%28a+-+b%29%2A%28a%5E2%2Bab%2Bb%5E2%29\"$ . You can use the distributive property to verify this.
\n" ); document.write( "Also, note that the quotient property of logarithms states: $\"log%28a%29-log%28b%29+=+log+%28a%2Fb%29\"$ .\r
\n" ); document.write( "\n" ); document.write( "First, replace $\"x%5E3+-+8\"$ with $\"x%5E3+-+2%5E3\"$ .
\n" ); document.write( "Use the first property I explained. This will simplify to
\n" ); document.write( " $\"log%28%28x-2%29%28x%5E2%2B2x%2B4%29%29+-+log+%28x-2%29\"$ .
\n" ); document.write( "Use the second property.
\n" ); document.write( " $\"log%28%28%28x-2%29%28x%5E2%2B2x%2B4%29%29%2F%28x-2%29%29\"$ .
\n" ); document.write( "Simplify by canceling the $\"x-2\"$ and you are left with the answer:
\n" ); document.write( " $\"log%28x%5E2%2B2x%2B4%29\"$
\n" ); document.write( " NtNk \n" ); document.write( "

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