# Determine rationality of an expression?

I am trying to determine whether an expression is rational or not - and if it rational, to get the numerator and denominator.

To give you some context, I first use "solve" to get a `[ x == ..., y == ... ]`

solution, and then I compute `log(solution[x])/log(solution[y])`

. In some cases, this expression is a rational. I would like to be able to determine when it is a rational.

Of course it is rational in some very predictable cases - i.e., when the two logarithms are commensurate, and there are ways of checking this on the value of `solution[x]`

and `solution[y]`

themselves. But I am hoping that sage can do this for me.

I tried to do `Rational((log(...)/log(...)).n())`

or `(log(...)/log(...)).n() in QQ`

, but of course that does not work, as `.n()`

converts the expression to some arbitrary precision float. Doing `(log(...)/log(...)) in QQ`

always returns False even, for instance, for the case `(log(100)/log(10)) = 2`

.

How can I do this?