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

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domain of 1/(ln(x))

domain

\frac{1}{ln ( x )}

0 < x < 1 or x > 1

Interval Notation

(0, 1) \cup (1, \infty)

Solution steps

Find positive values for logs:

x > 0

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

0 < x < 1 or x > 1

f (x) = - x - 5

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

f (y) = \frac{4}{y - 2}

f (x) = 2 x + 2

f (x) = \frac{2 x - 5}{x - 3}