What is the domain of f(x)=x^{ln(x)} ?

The domain of f(x)=x^{ln(x)} is x>0

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domain of f(x)=x^{ln(x)}

domain

f (x) = x^{l n (x)}

x > 0

Interval Notation

(0, \infty)

Solution steps

Find positive values for logs:

x > 0

Check exponents domain:

x > 0

Combine real regions and undefined points for final function domain

x > 0

f (x) = 2 + 3 x^{2} - x^{3}

f (x) = \frac{1 - 6 x + 9 x ^{2}}{3 x - 1}

f (x) = \frac{4 x + 10}{x + 3}

f (x) = - x^{2} - 16

f (x) = \frac{1 - x}{x ^{2} - 4}