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

The domain of f(x)= x/(ln(x-1)-1) is 1 e+1

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

domain

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

1 < x < e + 1 or x > e + 1

Interval Notation

(1, e + 1) \cup (e + 1, \infty)

Solution steps

Find positive values for logs:

x > 1

Find undefined (singularity) points:

x = e + 1

Combine real regions and undefined points for final function domain

1 < x < e + 1 or x > e + 1

y = 4 csc (x - \frac{π}{6}) + 5

f (x) = 20 x - 1740

\frac{x}{2} - 3

f (x) = \frac{x ^{2} - 5 x + 6}{x + 4}

ln ∣ x - 3 ∣ \cdot (x - 1) (5 - x)

What is the domain of f(x)= x/(ln(x-1)-1) ?
The domain of f(x)= x/(ln(x-1)-1) is 1<x<e+1\lor x>e+1