What is the domain of f(x)=log_{5}((x+6)/x) ?

The domain of f(x)=log_{5}((x+6)/x) is x 0

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domain of f(x)=log_{5}((x+6)/x)

domain

f (x) = lo g_{5} (\frac{x + 6}{x})

x < - 6 or x > 0

Interval Notation

(- \infty, - 6) \cup (0, \infty)

Solution steps

Find positive values for logs:

x < - 6 or x > 0

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x < - 6 or x > 0

\frac{x ^{2} - 4}{2 x ^{2} - 1}

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

f (x) = \frac{- 8 - y ^{2}}{2}

f (t) = ln (t + 2)

f (x) = x 2 + x

What is the domain of f(x)=log_{5}((x+6)/x) ?
The domain of f(x)=log_{5}((x+6)/x) is x<-6\lor x>0