What is the domain of ln(sqrt(((x-3))/(x-1))) ?

The domain of ln(sqrt(((x-3))/(x-1))) is x 3

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domain of ln(sqrt(((x-3))/(x-1)))

domain

ln (\frac{( x - 3 )}{x - 1})

x < 1 or x > 3

Interval Notation

(- \infty, 1) \cup (3, \infty)

Solution steps

Find positive values for logs:

x < 1 or x > 3

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

x < 1 or x > 3

\frac{sin ^{2} ( 4 x )}{[ 5 x \cdot sin ( 3 x ) ]}

y = x^{2} - 12

f (x) = - \frac{x}{12}

x^{\frac{3}{4}}

f (x) = 8 x^{2} + 9

What is the domain of ln(sqrt(((x-3))/(x-1))) ?
The domain of ln(sqrt(((x-3))/(x-1))) is x<1\lor x>3