What is the domain of log_{3}((x+1)/(x-5)) ?

The domain of log_{3}((x+1)/(x-5)) is x 5

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domain of log_{3}((x+1)/(x-5))

domain

lo g_{3} (\frac{x + 1}{x - 5})

x < - 1 or x > 5

Interval Notation

(- \infty, - 1) \cup (5, \infty)

Solution steps

Find positive values for logs:

x < - 1 or x > 5

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

x < - 1 or x > 5

lo g_{10} (x^{2} - 4)

- \frac{1}{x ^{2} + 6 x - 7}

\frac{2}{3} x - 4

f (x) = \frac{2 x + 3}{x - 5}

\frac{x + 2}{x ^{2} - 2 x - 3}

What is the domain of log_{3}((x+1)/(x-5)) ?
The domain of log_{3}((x+1)/(x-5)) is x<-1\lor x>5