What is the domain of f(x)=(ln(5x))/x ?

The domain of f(x)=(ln(5x))/x is x>0

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domain of f(x)=(ln(5x))/x

domain

f (x) = \frac{ln ( 5 x )}{x}

x > 0

Interval Notation

(0, \infty)

Solution steps

Find positive values for logs:

x > 0

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x > 0

f (x) = \frac{x ^{2} + 1}{x ^{2} + 5}

y = x^{2} + 8

y = \frac{6 + x}{3 - x}

f (x) = 3 x + \frac{5}{4}

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