What is the domain of f(x)=ln((x+3)/(x-3)) ?

The domain of f(x)=ln((x+3)/(x-3)) is x 3

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domain of f(x)=ln((x+3)/(x-3))

domain

f (x) = ln (\frac{x + 3}{x - 3})

x < - 3 or x > 3

Interval Notation

(- \infty, - 3) \cup (3, \infty)

Solution steps

Find positive values for logs:

x < - 3 or x > 3

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x < - 3 or x > 3

What is the domain of f(x)=ln((x+3)/(x-3)) ?
The domain of f(x)=ln((x+3)/(x-3)) is x<-3\lor x>3