I would like to solve an equation like this $\frac{\log(2)}{\log(3)}=\frac{n-0.5}{k-0.5}$ where $n$, $k$ are positive integers and $\log$ is natural logarithm. Of course, I can do only numerical approximation, because $\log(2)$ is not a rational number (transcendental), but if I tell to Mathematica NSolve
with assumptions $n$, $k$ integers, then it does not work or return me not integer values for $n$ and $k$.
Also, I understand that it is not 100% proper equation, because there are 2 variables and 1 equation, but I need to get any $n$ and $k$ which will make it equals or minimum possible integer $n$, $k$ with the specified precision. But maybe there is a way...
{n,k}
and the closeness of approximation. $\endgroup$