# Domain of One Variable Function – A function with log – Exercise 5744

Exercise

Determine the domain of the function:

$$y=\log_a (x+2)+\log_a (x-2)$$

$$x>2$$

Solution

Let’s find the domain of the function:

$$y=\log_a (x+2)+\log_a (x-2)$$

Because there is a log, we need the expressions inside the log to be greater than zero:

$$x+2>0\text{ and }x-2>0$$

We isolate the x in both inequalities and get:

$$x>-2\text{ and }x>2$$

Intersect both results (“and”) and get the final answer:

$$x>2$$

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