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

The domain of (ln(x)+1)/(ln(x)-1) is 0 e

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

domain

\frac{ln ( x ) + 1}{ln ( x ) - 1}

0 < x < e or x > e

Interval Notation

(0, e) \cup (e, \infty)

Solution steps

Find positive values for logs:

x > 0

Find undefined (singularity) points:

x = e

Combine real regions and undefined points for final function domain

0 < x < e or x > e

What is the domain of (ln(x)+1)/(ln(x)-1) ?
The domain of (ln(x)+1)/(ln(x)-1) is 0<x<e\lor x>e