What is the domain of log_{a}(x^2-4) ?

The domain of log_{a}(x^2-4) is (x 1))\lor (x>2\land (0 1))

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domain of log_{a}(x^2-4)

domain

lo g_{a} (x^{2} - 4)

(x < - 2 and (0 < a < 1 or a > 1)) or (x > 2 and (0 < a < 1 or a > 1))

Interval Notation

(x \in (- \infty, - 2) \cap (a \in (0, 1) \cup a \in (1, \infty))) \cup (x \in (2, \infty) \cap (a \in (0, 1) \cup a \in (1, \infty)))

Solution steps

Check logs domain:

(x < - 2 and (0 < a < 1 or a > 1)) or (x > 2 and (0 < a < 1 or a > 1))

The function domain

(x < - 2 and (0 < a < 1 or a > 1)) or (x > 2 and (0 < a < 1 or a > 1))

f (x) = 5 x^{2} ln (\frac{x}{2})

f (x) = \frac{x}{49 + x ^{2}}

f (x) = 3 x + 1

f (x) = 25 - x^{2} + x + 3

f (x) = 6 sin (3 x)

What is the domain of log_{a}(x^2-4) ?
The domain of log_{a}(x^2-4) is (x<-2\land (0<a<1\lor a>1))\lor (x>2\land (0<a<1\lor a>1))