What is the domain of f(x)=ln(x/(x-3)) ?

The domain of f(x)=ln(x/(x-3)) is x 3

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domain of f(x)=ln(x/(x-3))

domain

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

x < 0 or x > 3

Interval Notation

(- \infty, 0) \cup (3, \infty)

Solution steps

Find positive values for logs:

x < 0 or x > 3

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x < 0 or x > 3

f (x) = x + sin (x) + x (x - 1)

2 π r^{2} + 12 π r

f (x) = - 2^{- x} + 6

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

f (x) = \frac{( x + 2 )}{( x ^{3} - 100 x )}

What is the domain of f(x)=ln(x/(x-3)) ?
The domain of f(x)=ln(x/(x-3)) is x<0\lor x>3