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

The domain of y=ln((3x-1)/(1-x)) is 1/3 <x<1

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domain of y=ln((3x-1)/(1-x))

domain

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

\frac{1}{3} < x < 1

Interval Notation

(\frac{1}{3}, 1)

Solution steps

Find positive values for logs:

\frac{1}{3} < x < 1

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

\frac{1}{3} < x < 1

x + y = 353

f (x) = \frac{1}{x ^{2} + x - 6}

y = - 5 x

f (x) = (- x^{2} + 16) (x + 1)

(1, - 4), (11, 8)

What is the domain of y=ln((3x-1)/(1-x)) ?
The domain of y=ln((3x-1)/(1-x)) is 1/3 <x<1