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

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

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

domain

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

f (x) = 4 cos (\frac{1}{x})

- x^{2}

\frac{d}{d}

f (x) = 2 x^{2} - 12 x + 9

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