What is the domain of ln(sqrt((x-8)/(x-4))) ?

The domain of ln(sqrt((x-8)/(x-4))) is x 8

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domain of ln(sqrt((x-8)/(x-4)))

domain

ln (\frac{x - 8}{x - 4})

x < 4 or x > 8

Interval Notation

(- \infty, 4) \cup (8, \infty)

Solution steps

Find positive values for logs:

x < 4 or x > 8

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

x < 4 or x > 8

What is the domain of ln(sqrt((x-8)/(x-4))) ?
The domain of ln(sqrt((x-8)/(x-4))) is x<4\lor x>8