What is the domain of f(x)= x/(1-ln(x-3)) ?

The domain of f(x)= x/(1-ln(x-3)) is 3 e+3

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domain of f(x)= x/(1-ln(x-3))

domain

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

3 < x < e + 3 or x > e + 3

Interval Notation

(3, e + 3) \cup (e + 3, \infty)

Solution steps

Find positive values for logs:

x > 3

Find undefined (singularity) points:

x = e + 3

Combine real regions and undefined points for final function domain

3 < x < e + 3 or x > e + 3

f (x) = \frac{3}{2 x - 8}

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

f (x) = \frac{2}{x ^{3} - 4 x}

\frac{1}{x ^{2} + 4}

f (x) = \frac{3 x - 4}{7}

What is the domain of f(x)= x/(1-ln(x-3)) ?
The domain of f(x)= x/(1-ln(x-3)) is 3<x<e+3\lor x>e+3