What is the domain of f(x)=ln|x|-1/2 ln|x^2+1| ?

The domain of f(x)=ln|x|-1/2 ln|x^2+1| is x 0

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domain of f(x)=ln|x|-1/2 ln|x^2+1|

domain

f (x) = ln ∣ x ∣ - \frac{1}{2} ln x^{2} + 1

x < 0 or x > 0

Interval Notation

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

Solution steps

Find positive values for logs:

x < 0 or x > 0

The function domain

x < 0 or x > 0

\frac{1}{2} ln (3) - ln (2) - ln (\frac{1}{2})

ln (e) - ln (1000) + lo g_{2} (32)

ln (\frac{999999950}{0.00000001})

f (x) = lo g_{10} (0.3 x)

f (x) = ln (5 x) + ln (2 x)

What is the domain of f(x)=ln|x|-1/2 ln|x^2+1| ?
The domain of f(x)=ln|x|-1/2 ln|x^2+1| is x<0\lor x>0