What is the domain of f(x)= 1/(1+ln(x-2)) ?

The domain of f(x)= 1/(1+ln(x-2)) is 2 1/e+2

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domain of f(x)= 1/(1+ln(x-2))

domain

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

2 < x < \frac{1}{e} + 2 or x > \frac{1}{e} + 2

Interval Notation

(2, \frac{1}{e} + 2) \cup (\frac{1}{e} + 2, \infty)

Solution steps

Find positive values for logs:

x > 2

Find undefined (singularity) points:

x = \frac{1}{e} + 2

Combine real regions and undefined points for final function domain

2 < x < \frac{1}{e} + 2 or x > \frac{1}{e} + 2

3 - lo g_{10} (x^{2} - 1)

\frac{2}{3 + x}

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

csc (- 2 x)

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

What is the domain of f(x)= 1/(1+ln(x-2)) ?
The domain of f(x)= 1/(1+ln(x-2)) is 2<x< 1/e+2\lor x> 1/e+2