SOLUTION: express as a single logarithm and if possible simplify log(x^2+x-6)-log(x^2-9)

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Question 865315: express as a single logarithm and if possible simplify
log(x^2+x-6)-log(x^2-9)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%28x%5E2%2Bx-6%29%29-log%28%28x%5E2-9%29%29


log%28%28%28x%5E2%2Bx-6%29%2F%28x%5E2-9%29%29%29 Use rule 2 from this page


log%28%28%28%28x%2B3%29%28x-2%29%29%2F%28x%5E2-9%29%29%29 Factor the numerator


log%28%28%28%28x%2B3%29%28x-2%29%29%2F%28%28x-3%29%28x%2B3%29%29%29%29 Factor the denominator


Highlight common terms


log%28%28%28cross%28%28x%2B3%29%29%28x-2%29%29%2F%28%28x-3%29cross%28%28x%2B3%29%29%29%29%29 Cancel out those common terms (they divide to 1 and go away, since 1*any number = any number)


log%28%28%28x-2%29%2F%28x-3%29%29%29


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So log%28%28x%5E2%2Bx-6%29%29-log%28%28x%5E2-9%29%29 simplifies to log%28%28%28x-2%29%2F%28x-3%29%29%29