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

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

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

domain

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

1 < x < 3

Interval Notation

(1, 3)

Solution steps

Find positive values for logs:

1 < x < 3

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

1 < x < 3

f (x) = \frac{x - 15}{x ^{3} + 4 x}

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

f (x) = 9 x - 3

\frac{1 + x}{x}

f (x) = 7 x^{4} + 5 x

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