What is the domain of f(x)=log_{10}((x+2)/(x-4)) ?

The domain of f(x)=log_{10}((x+2)/(x-4)) is x 4

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domain of f(x)=log_{10}((x+2)/(x-4))

domain

x < - 2 or x > 4

Interval Notation

(- \infty, - 2) \cup (4, \infty)

Solution steps

Find positive values for logs:

x < - 2 or x > 4

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

x < - 2 or x > 4

What is the domain of f(x)=log_{10}((x+2)/(x-4)) ?
The domain of f(x)=log_{10}((x+2)/(x-4)) is x<-2\lor x>4