What is the domain of f(x)=log_{10}((x-2)/(x^2-5)) ?

The domain of f(x)=log_{10}((x-2)/(x^2-5)) is -sqrt(5) sqrt(5)

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domain of f(x)=log_{10}((x-2)/(x^2-5))

domain

f (x) = lo g_{10} (\frac{x - 2}{x ^{2} - 5})

- 5 < x < 2 or x > 5

Interval Notation

(- 5, 2) \cup (5, \infty)

Solution steps

Find positive values for logs:

- 5 < x < 2 or x > 5

Find undefined (singularity) points:

x = 5, x = - 5

Combine real regions and undefined points for final function domain

- 5 < x < 2 or x > 5

f (x) = ln (2 + x)

f (x) = 5 x^{4} - 14

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

f (x) = x y - y - 1 = 0

What is the domain of f(x)=log_{10}((x-2)/(x^2-5)) ?
The domain of f(x)=log_{10}((x-2)/(x^2-5)) is -sqrt(5)<x<2\lor x>sqrt(5)