SOLUTION: Expand : log[(x^2+6x+9)/(x^2-9)] I could really use some help with this.

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Question 409974: Expand : log[(x^2+6x+9)/(x^2-9)]
I could really use some help with this.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%28%28x%5E2%2B6x%2B9%29%2F%28x%5E2-9%29%29%29
First let's simplify the argument. We can reduce this fraction if we factor it:
log%28%28%28%28x%2B3%29%28x%2B3%29%29%2F%28x%2B3%29%28x-3%29%29%29
Now we can cancel the common factor:
log%28%28%28cross%28%28x%2B3%29%29%28x%2B3%29%29%2Fcross%28%28x%2B3%29%29%28x-3%29%29%29
log%28%28%28x%2B3%29%2F%28x-3%29%29%29
Now let's expand it. To expand it we will use a property of logarithms, log%28a%2C+%28p%2Fq%29%29+=+log%28a%2C+%28p%29%29+-+log%28a%2C+%28q%29%29, which allows us to split the log of a quotient into the difference of the logs of the numerator and denominator:
log%28%28x%2B3%29%29+-+log%28%28x-3%29%29