What is the domain of f(x)=ln(((5-x))/((4-x))) ?

The domain of f(x)=ln(((5-x))/((4-x))) is x 5

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domain of f(x)=ln(((5-x))/((4-x)))

domain

f (x) = ln (\frac{( 5 - x )}{( 4 - x )})

x < 4 or x > 5

Interval Notation

(- \infty, 4) \cup (5, \infty)

Solution steps

Find positive values for logs:

x < 4 or x > 5

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

x < 4 or x > 5

What is the domain of f(x)=ln(((5-x))/((4-x))) ?
The domain of f(x)=ln(((5-x))/((4-x))) is x<4\lor x>5