Find the domain of the logarithmic function. f(x) = log(x+5/x-2)

Question

Show all steps. The equation is f(x)=log (x+5 over x-2)

Answer 1

f(x) = log[(x+5)/(x-2)]

 

Domain = {x l (x+5)/(x-2) > 0}

 

There are 2 cases to consider:

 

   Case 1:  x+5>0 and x-2>0

 

                So, x>-5 and x>2

 

                Therefore, x>2

 

   Case 2:  x+5<0 and x-2<0

 

                So, x<-5 and x< 2

 

                Therefore, x<-5

 

Domain:  (-∞,-5) ∪ (2,∞)