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

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

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

domain

\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

y = lo g_{x} (36 - x^{2})

6 x

f (x) = \frac{x - 5}{x ^{2} - 64}

arcsin (\frac{x - 8}{9}) + 5

\frac{4 - 9 x}{x ^{2} + 3 x - 40}

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