Math CentralQuandaries & Queries


Question from Behrooz, a teacher:

Hi, the following problem may be interesting:

What is the domain of f(x)=sin(ln(x))/ln(x)?
Be careful, domain is not obvious.

Hi Behrooz,

When I first look at

\[f(x) \ \frac{\sin(\ln x)}{\ln x}\]

I see the log function and $\ln x$ has the positive real numbers as its domain. Thus the domain of $f(x)$ can't contain zero or any negative numbers.

The sine function is not a problem since its domain is the real numbers and thus, as long as $\ln x$ is a real number so is $\sin( \ln x).$ But you have a fraction and the denominator can't be zero. What value(s) of $x$ make the denominator zero?


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