What is the domain of y= 1/(log_{10)(|x|)} ?

The domain of y= 1/(log_{10)(|x|)} is x 1

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domain of y= 1/(log_{10)(|x|)}

domain

x < - 1 or - 1 < x < 0 or 0 < x < 1 or x > 1

Interval Notation

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

Solution steps

Find positive values for logs:

x < 0 or x > 0

Find undefined (singularity) points:

x = - 1, x = 1

Combine real regions and undefined points for final function domain

x < - 1 or - 1 < x < 0 or 0 < x < 1 or x > 1

What is the domain of y= 1/(log_{10)(|x|)} ?
The domain of y= 1/(log_{10)(|x|)} is x<-1\lor-1<x<0\lor 0<x<1\lor x>1