What is the domain of (log_{x}(2)-1)/(1-log_{3)(x)} ?

The domain of (log_{x}(2)-1)/(1-log_{3)(x)} is 0 3

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domain of (log_{x}(2)-1)/(1-log_{3)(x)}

domain

\frac{lo g _{x} ( 2 ) - 1}{1 - lo g _{3} ( x )}

0 < x < 1 or 1 < x < 3 or x > 3

Interval Notation

(0, 1) \cup (1, 3) \cup (3, \infty)

Solution steps

Find positive values for logs:

x > 0

Check value of logs base:

0 < x < 1 or x > 1

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

0 < x < 1 or 1 < x < 3 or x > 3

f (x) = 2 lo g_{2} (x - 1)

f (x) = 2 x^{2} + 3 x + 2

\frac{12 x - 9}{6 - 9 x}

f (x) = t + 9

f (x) = ∣ 2 - x ∣

What is the domain of (log_{x}(2)-1)/(1-log_{3)(x)} ?
The domain of (log_{x}(2)-1)/(1-log_{3)(x)} is 0<x<1\lor 1<x<3\lor x>3