3
votes
1answer
52 views

Rational values of $\sin(\log(x))$

Apart from the trivial solution $\sin(\log(1))=0$, is $$\sin(\log(x))$$ ever rational if $x$ is rational?
1
vote
3answers
66 views

If $\log_{b}N$ is rational, what are the limitations on the possible values of $b$ and $N$?

If $\log_{b}N$ is rational, is there a set of values to which $b$ and $N$ must belong? Is there a set of values to which $b$ and $N$ cannot belong? Further, if it is presupposed that $b$ and $N$ are ...