What is the domain of f(x)= x/(1-ln(x-5)) ?

The domain of f(x)= x/(1-ln(x-5)) is 5 e+5

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domain of f(x)= x/(1-ln(x-5))

domain

f (x) = \frac{x}{1 - ln ( x - 5 )}

5 < x < e + 5 or x > e + 5

Interval Notation

(5, e + 5) \cup (e + 5, \infty)

Solution steps

Find positive values for logs:

x > 5

Find undefined (singularity) points:

x = e + 5

Combine real regions and undefined points for final function domain

5 < x < e + 5 or x > e + 5

\frac{1}{x + 36}

f (x) = y + 6

f (x) = 3 x^{2} + 7 x + 2

f (x) = x^{\frac{1}{3}} (x^{2} - 63)

(\frac{2}{3})^{x - 3} - 2

What is the domain of f(x)= x/(1-ln(x-5)) ?
The domain of f(x)= x/(1-ln(x-5)) is 5<x<e+5\lor x>e+5