What is the domain of f(x)=(ln(1+|x+3|))/(ln(x)) ?

The domain of f(x)=(ln(1+|x+3|))/(ln(x)) is 0 1

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domain of f(x)=(ln(1+|x+3|))/(ln(x))

domain

f (x) = \frac{ln ( 1 + ∣ x + 3 ∣ )}{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

(- 4, 2), (6, 4)

y = \frac{8}{x ^{2} - 6 x + 8}

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

(- 4, 3), (- 2, 1)

What is the domain of f(x)=(ln(1+|x+3|))/(ln(x)) ?
The domain of f(x)=(ln(1+|x+3|))/(ln(x)) is 0<x<1\lor x>1