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# How do you find the domain of this log problem?

f(x)= log ((x-3)(x+5)^2(x+7) / (x-6)(x-9)^2(10-x)) If you could help it would be greatly appreciated!

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- Anonymous9 years agoFavorite Answer
The domain is the set of x values in which f(x) exist. For this problem, the x values that yield nonexisting value make f(x) ≤ 0. In order to make f(x) existing, let the inside expression be > 0, so...

(x - 3)(x + 5)²(x + 7)/((x - 6)(x - 9)²(10 - x)) > 0

You can solve this expression algebraically or graphically.

The answers are...

-7 < x < -5, -5 < x < 3, 6 < x < 9, 9 < x < 10

I hope this helps!

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