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

Exercise

Determine the domain of the function:

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

Final Answer

Show final answer

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

$x>3$

Have a question? Found a mistake? – Write a comment below!
Was it helpful? You can buy me a cup of coffee here, which will make me very happy and will help me upload more solutions!