What is the domain of f(x)=log_{2}((2/(3x))-4) ?

The domain of f(x)=log_{2}((2/(3x))-4) is 0<x< 1/6

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domain of f(x)=log_{2}((2/(3x))-4)

domain

f (x) = lo g_{2} ((\frac{2}{3 x}) - 4)

0 < x < \frac{1}{6}

Interval Notation

(0, \frac{1}{6})

Solution steps

Find positive values for logs:

0 < x < \frac{1}{6}

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

0 < x < \frac{1}{6}

(x - 7) (x - 9)

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

\frac{19 x}{x - 3}

g (x) = 3 x + 1

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

What is the domain of f(x)=log_{2}((2/(3x))-4) ?
The domain of f(x)=log_{2}((2/(3x))-4) is 0<x< 1/6