Domain of One Variable Function – A function with sum of ln’s – Exercise 2443

Exercise

Determine the domain of the function:

$$f(x)=\ln (x+2)+\ln (x-3)$$

$$x>3$$

Solution

Let’s find the domain of the function:

$$f(x)=\ln (x+2)+\ln (x-3)$$

Because there are ln’s, we need the expressions inside the ln’s to be greater than zero:

$$x+2>0\text{ and }x-3>0$$

We got two inequalities. We’ll arrange them:

$$x+2>0 \Longrightarrow x>-2$$

$$x-3>0 \Longrightarrow x>3$$

Intersect both inequalities:

$$x>-2 \text{ and } x>3 \Longrightarrow x>3$$

Hence, the domain of the function is

$$x>3$$

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