What is the domain of f(x)=(x-1)/(ln(x-2)) ?

The domain of f(x)=(x-1)/(ln(x-2)) is 2 3

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domain of f(x)=(x-1)/(ln(x-2))

domain

f (x) = \frac{x - 1}{ln ( x - 2 )}

2 < x < 3 or x > 3

Interval Notation

(2, 3) \cup (3, \infty)

Solution steps

Find positive values for logs:

x > 2

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

2 < x < 3 or x > 3

y = lo g_{8} (x)

f (x) = - 2 x (x - 2) (x - 7)

f (x) = 6 + ln (x)

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

lo g_{4} (x - 1)

What is the domain of f(x)=(x-1)/(ln(x-2)) ?
The domain of f(x)=(x-1)/(ln(x-2)) is 2<x<3\lor x>3