SOLUTION: Express as a single logarithm and, if possible simplify log(x^3-8)-log(x-2)

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Question 33712: Express as a single logarithm and, if possible simplify
log(x^3-8)-log(x-2)
Answer by ntnk(54) About Me  (Show Source):
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.
Also, note that the quotient property of logarithms states: log%28a%29-log%28b%29+=+log+%28a%2Fb%29.
First, replace x%5E3+-+8 with x%5E3+-+2%5E3.
Use the first property I explained. This will simplify to
log%28%28x-2%29%28x%5E2%2B2x%2B4%29%29+-+log+%28x-2%29.
Use the second property.
log%28%28%28x-2%29%28x%5E2%2B2x%2B4%29%29%2F%28x-2%29%29.
Simplify by canceling the x-2 and you are left with the answer:
log%28x%5E2%2B2x%2B4%29
NtNk