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

The domain of f(x)= 1/(ln(x-1)) is 1 2

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

domain

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

1 < x < 2 or x > 2

Interval Notation

(1, 2) \cup (2, \infty)

Solution steps

Find positive values for logs:

x > 1

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

1 < x < 2 or x > 2

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

y = \frac{1}{2} x + 5

2 x + 7

f (x) = \frac{x ^{2} - 2 x - 8}{x + 1}

f (x) = 9 x + 8

What is the domain of f(x)= 1/(ln(x-1)) ?
The domain of f(x)= 1/(ln(x-1)) is 1<x<2\lor x>2