What is the domain of f(x)= x/(1-ln(x-4)) ?

The domain of f(x)= x/(1-ln(x-4)) is 4 e+4

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domain of f(x)= x/(1-ln(x-4))

domain

f (x) = \frac{x}{1 - ln ( x - 4 )}

4 < x < e + 4 or x > e + 4

Interval Notation

(4, e + 4) \cup (e + 4, \infty)

Solution steps

Find positive values for logs:

x > 4

Find undefined (singularity) points:

x = e + 4

Combine real regions and undefined points for final function domain

4 < x < e + 4 or x > e + 4

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

(8 + 60) (6 + 160)

(0, 0), (10, 5)

f (x) = x^{3} - 8

(- 5, 2), (3, 6)

What is the domain of f(x)= x/(1-ln(x-4)) ?
The domain of f(x)= x/(1-ln(x-4)) is 4<x<e+4\lor x>e+4