What is the domain of log_{6}((x-8)/x) ?

The domain of log_{6}((x-8)/x) is x 8

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domain of log_{6}((x-8)/x)

domain

lo g_{6} (\frac{x - 8}{x})

x < 0 or x > 8

Interval Notation

(- \infty, 0) \cup (8, \infty)

Solution steps

Find positive values for logs:

x < 0 or x > 8

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x < 0 or x > 8

x^{2} (x + 1)^{3} (x - 3)

\frac{1}{4 x - 1} - 1 - x^{2}

\frac{x - 2}{x ^{2}}

y = - 2^{x} - 1

∣ x ∣ ∣ x - 1 ∣

What is the domain of log_{6}((x-8)/x) ?
The domain of log_{6}((x-8)/x) is x<0\lor x>8