What is the domain of f(x)=log_{10}((x+3)/(x-7)) ?

The domain of f(x)=log_{10}((x+3)/(x-7)) is x 7

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domain of f(x)=log_{10}((x+3)/(x-7))

domain

f (x) = lo g_{10} (\frac{x + 3}{x - 7})

x < - 3 or x > 7

Interval Notation

(- \infty, - 3) \cup (7, \infty)

Solution steps

Find positive values for logs:

x < - 3 or x > 7

Find undefined (singularity) points:

x = 7

Combine real regions and undefined points for final function domain

x < - 3 or x > 7

f (x) = \frac{x + 34}{4}

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

y = \frac{x}{x + 2} - \frac{x}{x - 2}

x^{2} - 6 x - 3

f (x) = \frac{10}{x ^{2} + 1}

What is the domain of f(x)=log_{10}((x+3)/(x-7)) ?
The domain of f(x)=log_{10}((x+3)/(x-7)) is x<-3\lor x>7