What is the domain of log_{5}(x/(x+1)) ?

The domain of log_{5}(x/(x+1)) is x 0

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domain of log_{5}(x/(x+1))

domain

lo g_{5} (\frac{x}{x + 1})

x < - 1 or x > 0

Interval Notation

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

Solution steps

Find positive values for logs:

x < - 1 or x > 0

Find undefined (singularity) points:

x = - 1

Combine real regions and undefined points for final function domain

x < - 1 or x > 0

\frac{1}{3 - x}

f (x) = - \frac{x}{2} + 3

\frac{x}{x}

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

f (x) = \frac{x - 3}{x ^{2} - 4 x + 3}

What is the domain of log_{5}(x/(x+1)) ?
The domain of log_{5}(x/(x+1)) is x<-1\lor x>0