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

The domain of f(x)= 1/(ln(x+sqrt(x))) is 0 (3-sqrt(5))/2

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domain of f(x)= 1/(ln(x+sqrt(x)))

domain

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

0 < x < \frac{3 - 5}{2} or x > \frac{3 - 5}{2}

Interval Notation

(0, \frac{3 - 5}{2}) \cup (\frac{3 - 5}{2}, \infty)

Solution steps

Find positive values for logs:

x > 0

Find undefined (singularity) points:

x = \frac{3 - 5}{2}

Combine real regions and undefined points for final function domain

0 < x < \frac{3 - 5}{2} or x > \frac{3 - 5}{2}

f (x) = - 2 + ln (x)

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

f (x) = ln (x^{2} + 4)

f (x) = \frac{x + 1}{x}

\frac{x + 5}{1 - x - 2}

What is the domain of f(x)= 1/(ln(x+sqrt(x))) ?
The domain of f(x)= 1/(ln(x+sqrt(x))) is 0<x<(3-sqrt(5))/2 \lor x>(3-sqrt(5))/2