What is the domain of f(x)=(ln(x-2))/(x-5) ?

The domain of f(x)=(ln(x-2))/(x-5) is 2 5

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domain of f(x)=(ln(x-2))/(x-5)

domain

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

2 < x < 5 or x > 5

Interval Notation

(2, 5) \cup (5, \infty)

Solution steps

Find positive values for logs:

x > 2

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

2 < x < 5 or x > 5

- x + 49

\frac{6 x - 5}{3}

2 x^{2} + 7 x

f (x) = \frac{7 x}{x + 3}

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

What is the domain of f(x)=(ln(x-2))/(x-5) ?
The domain of f(x)=(ln(x-2))/(x-5) is 2<x<5\lor x>5