What is the domain of (\sqrt[8]{x-2})/(log_{4)(5-x)} ?

The domain of (\sqrt[8]{x-2})/(log_{4)(5-x)} is 2<= x<4\lor 4<x<5

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domain of (\sqrt[8]{x-2})/(log_{4)(5-x)}

domain

2 \leq x < 4 or 4 < x < 5

Interval Notation

[2, 4) \cup (4, 5)

Solution steps

Find non-negative values for radicals:

x \geq 2

Find positive values for logs:

x < 5

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

2 \leq x < 4 or 4 < x < 5

What is the domain of (\sqrt[8]{x-2})/(log_{4)(5-x)} ?
The domain of (\sqrt[8]{x-2})/(log_{4)(5-x)} is 2<= x<4\lor 4<x<5