What is the domain of (log_{2}(x-4))/(log_{2)(7-x)} ?

The domain of (log_{2}(x-4))/(log_{2)(7-x)} is 4<x<6\lor 6<x<7

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domain of (log_{2}(x-4))/(log_{2)(7-x)}

domain

\frac{lo g _{2} ( x - 4 )}{lo g _{2} ( 7 - x )}

4 < x < 6 or 6 < x < 7

Interval Notation

(4, 6) \cup (6, 7)

Solution steps

Find positive values for logs:

4 < x < 7

Find undefined (singularity) points:

x = 6

Combine real regions and undefined points for final function domain

4 < x < 6 or 6 < x < 7

What is the domain of (log_{2}(x-4))/(log_{2)(7-x)} ?
The domain of (log_{2}(x-4))/(log_{2)(7-x)} is 4<x<6\lor 6<x<7