What is the domain of f(x)= x/(1-ln(x-6)) ?

The domain of f(x)= x/(1-ln(x-6)) is 6 e+6

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domain of f(x)= x/(1-ln(x-6))

domain

f (x) = \frac{x}{1 - ln ( x - 6 )}

6 < x < e + 6 or x > e + 6

Interval Notation

(6, e + 6) \cup (e + 6, \infty)

Solution steps

Find positive values for logs:

x > 6

Find undefined (singularity) points:

x = e + 6

Combine real regions and undefined points for final function domain

6 < x < e + 6 or x > e + 6

\frac{3 x}{x ^{2} - 4}

f (x) = \frac{- 1}{2 3 - x}

f (x) = 2 sin (x)

f (x) = 8 x^{3}

f (x) = \frac{- 3 x + 7}{7 x - 2}

What is the domain of f(x)= x/(1-ln(x-6)) ?
The domain of f(x)= x/(1-ln(x-6)) is 6<x<e+6\lor x>e+6