What is the domain of f(x)= x/(1-ln(x-8)) ?

The domain of f(x)= x/(1-ln(x-8)) is 8 e+8

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domain of f(x)= x/(1-ln(x-8))

domain

f (x) = \frac{x}{1 - ln ( x - 8 )}

8 < x < e + 8 or x > e + 8

Interval Notation

(8, e + 8) \cup (e + 8, \infty)

Solution steps

Find positive values for logs:

x > 8

Find undefined (singularity) points:

x = e + 8

Combine real regions and undefined points for final function domain

8 < x < e + 8 or x > e + 8

f (x) = 2^{x - 5} - 11

\frac{x - 2}{x ^{2} + x - 6}

f (y) = x - 3 y = 6

(x + 3)^{2}

3 + 2 sin (5 x + \frac{π}{4})

What is the domain of f(x)= x/(1-ln(x-8)) ?
The domain of f(x)= x/(1-ln(x-8)) is 8<x<e+8\lor x>e+8