What is the domain of f(x)=(3x-ln(5x))/x ?

The domain of f(x)=(3x-ln(5x))/x is x>0

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domain of f(x)=(3x-ln(5x))/x

domain

f (x) = \frac{3 x - 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) = 3 x - 3 + 4 - x^{2} - 11 - x - 2

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

f (x) = \frac{x - 4}{5 - 2 x}

- \frac{2}{5} x + 6

3 x^{2} + 5

What is the domain of f(x)=(3x-ln(5x))/x ?
The domain of f(x)=(3x-ln(5x))/x is x>0