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

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

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

domain

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

2 < x < e + 2 or x > e + 2

Interval Notation

(2, e + 2) \cup (e + 2, \infty)

Solution steps

Find positive values for logs:

x > 2

Find undefined (singularity) points:

x = e + 2

Combine real regions and undefined points for final function domain

2 < x < e + 2 or x > e + 2

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<e+2\lor x>e+2