What is the domain of ln((x+4)/(4x-16)) ?

The domain of ln((x+4)/(4x-16)) is x 4

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domain of ln((x+4)/(4x-16))

domain

ln (\frac{x + 4}{4 x - 16})

x < - 4 or x > 4

Interval Notation

(- \infty, - 4) \cup (4, \infty)

Solution steps

Find positive values for logs:

x < - 4 or x > 4

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

x < - 4 or x > 4

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

f (x) = 2 x + 6 + 2 - x

f (x) = 30 - 4 x + 2 x^{2}

f (x) = 6 9 - 8 x + 7

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

What is the domain of ln((x+4)/(4x-16)) ?
The domain of ln((x+4)/(4x-16)) is x<-4\lor x>4