What is the domain of f(x)= x/(1-ln(x-9)) ?

The domain of f(x)= x/(1-ln(x-9)) is 9 e+9

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domain of f(x)= x/(1-ln(x-9))

domain

f (x) = \frac{x}{1 - ln ( x - 9 )}

9 < x < e + 9 or x > e + 9

Interval Notation

(9, e + 9) \cup (e + 9, \infty)

Solution steps

Find positive values for logs:

x > 9

Find undefined (singularity) points:

x = e + 9

Combine real regions and undefined points for final function domain

9 < x < e + 9 or x > e + 9

f (x) = \frac{x + 1}{x}

f (x) = \frac{x}{x ^{2} - 25}

f (x) = x^{2} + 49

x

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

What is the domain of f(x)= x/(1-ln(x-9)) ?
The domain of f(x)= x/(1-ln(x-9)) is 9<x<e+9\lor x>e+9