How do you find the domain of ln(x^2-9)?

1 Answer
Oct 2, 2016

x<-3, x>3, (x in RR)

Explanation:

lnx is defined for all x>0

:. ln(x^2-9) is defined for (x^2-9)>0

x^2>9

abs x> sqrt9 -> abs x >3

Hence the domain of ln(x^2-9) is x<-3, x>3, (x in RR)

We can get a sense of this from the graph of ln(x^2-9) below:

graph{ln (x^2-9) [-12.66, 12.66, -6.32, 6.34]}