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

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

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

domain

y = \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

\frac{x ^{2} + x - 30}{x - 5}

y = 4^{x}

f (x) = \frac{∣ x ∣ - 3}{5 - ∣ x ∣}

\frac{x - 2}{3}

2 x - 2

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