Yes, it is continuous to its domain
Explanation:
In order to find the domain of the function we need to get the restrictions:
1. From natural log:
[tex]x>0[/tex]
2. From quotient:
[tex]x\neq 0[/tex]
Matching these two restrictions the domain is:
[tex]x\in (0,\infty)[/tex]
So the function is continuous to its domain because is defined for every x-value in the interval [tex](0, \infty)[/tex])
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