What is the domain of f(x)=(ln(2x-1))/((x+3)(x-5)) ?

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

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domain of f(x)=(ln(2x-1))/((x+3)(x-5))

domain

f (x) = \frac{ln ( 2 x - 1 )}{( x + 3 ) ( x - 5 )}

\frac{1}{2} < x < 5 or x > 5

Interval Notation

(\frac{1}{2}, 5) \cup (5, \infty)

Solution steps

Find positive values for logs:

x > \frac{1}{2}

Find undefined (singularity) points:

x = - 3, x = 5

Combine real regions and undefined points for final function domain

\frac{1}{2} < x < 5 or x > 5

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

f (x) = \frac{1}{tan ( 2 x ) - \frac{3}{3}}

(x + 4)^{4}

2 + 2, x > 2

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

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