What is the domain of (sqrt(x-3))/(ln(5-x)) ?

The domain of (sqrt(x-3))/(ln(5-x)) is 3<= x<4\lor 4<x<5

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domain of (sqrt(x-3))/(ln(5-x))

domain

\frac{x - 3}{ln ( 5 - x )}

3 \leq x < 4 or 4 < x < 5

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq 3

Find positive values for logs:

x < 5

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

3 \leq x < 4 or 4 < x < 5

What is the domain of (sqrt(x-3))/(ln(5-x)) ?
The domain of (sqrt(x-3))/(ln(5-x)) is 3<= x<4\lor 4<x<5