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

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

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

domain

f (x) = \frac{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

f (x) = x^{4} - 4 x^{2} + 2

f (x) = ln^{2} (x)

f (x) = - lo g_{8} (x - 1) - 2

x^{2} + 3 x - 3

g (x) = \frac{x + 6}{x ^{2} - 3 x - 18}

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