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

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Answer 1 · 2016-10-02T02:03:58

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

#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]}