What is the domain of ln(sqrt((x-9)/(x-7))) ?

The domain of ln(sqrt((x-9)/(x-7))) is x 9

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domain of ln(sqrt((x-9)/(x-7)))

domain

ln (\frac{x - 9}{x - 7})

x < 7 or x > 9

Interval Notation

(- \infty, 7) \cup (9, \infty)

Solution steps

Find positive values for logs:

x < 7 or x > 9

Find undefined (singularity) points:

x = 7

Combine real regions and undefined points for final function domain

x < 7 or x > 9

f (x) = 3 + 5 + 7 x

3 x - 2

f (x) = \frac{7 x}{x + 3}

f (x) = 2 x - 26

1 0^{2} - 3 x - 1

What is the domain of ln(sqrt((x-9)/(x-7))) ?
The domain of ln(sqrt((x-9)/(x-7))) is x<7\lor x>9