What is the domain of y=(ln|x|)/((x-3)) ?

The domain of y=(ln|x|)/((x-3)) is x 3

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domain of y=(ln|x|)/((x-3))

domain

y = \frac{ln ∣ x ∣}{( x - 3 )}

x < 0 or 0 < x < 3 or x > 3

Interval Notation

(- \infty, 0) \cup (0, 3) \cup (3, \infty)

Solution steps

Find positive values for logs:

x < 0 or x > 0

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x < 0 or 0 < x < 3 or x > 3

\frac{2 x}{3 x - 3}

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

f (x) = \frac{19 x}{x + 20}

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

What is the domain of y=(ln|x|)/((x-3)) ?
The domain of y=(ln|x|)/((x-3)) is x<0\lor 0<x<3\lor x>3