What is the domain of log_{10}((6x)/(x+5)) ?

The domain of log_{10}((6x)/(x+5)) is x 0

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domain of log_{10}((6x)/(x+5))

domain

lo g_{10} (\frac{6 x}{x + 5})

x < - 5 or x > 0

Interval Notation

(- \infty, - 5) \cup (0, \infty)

Solution steps

Find positive values for logs:

x < - 5 or x > 0

Find undefined (singularity) points:

x = - 5

Combine real regions and undefined points for final function domain

x < - 5 or x > 0

f (x) = \frac{5}{4 6 x}

f (x) = - 5 x^{2} + 8 x + 4

f (x) = 8 x + 4

f (x) = x + x - 4

f (x) = \frac{x + 7}{x + 3}

What is the domain of log_{10}((6x)/(x+5)) ?
The domain of log_{10}((6x)/(x+5)) is x<-5\lor x>0