What is the domain of (2x^2)/(ln|x|-2) ?

The domain of (2x^2)/(ln|x|-2) is x e^2

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domain of (2x^2)/(ln|x|-2)

domain

\frac{2 x ^{2}}{ln ∣ x ∣ - 2}

x < - e^{2} or - e^{2} < x < 0 or 0 < x < e^{2} or x > e^{2}

Interval Notation

(- \infty, - e^{2}) \cup (- e^{2}, 0) \cup (0, e^{2}) \cup (e^{2}, \infty)

Solution steps

Find positive values for logs:

x < 0 or x > 0

Find undefined (singularity) points:

x = - e^{2}, x = e^{2}

Combine real regions and undefined points for final function domain

x < - e^{2} or - e^{2} < x < 0 or 0 < x < e^{2} or x > e^{2}

What is the domain of (2x^2)/(ln|x|-2) ?
The domain of (2x^2)/(ln|x|-2) is x<-e^2\lor-e^2<x<0\lor 0<x<e^2\lor x>e^2