The function \(f\) is such that for any positive \(x\) and \(y\) the equality \(f (xy) = f (x) + f (y)\) holds. Find \(f (2007)\) if \(f (1/2007) = 1\).
Are there any irrational numbers \(a\) and \(b\) such that the degree of \(a^b\) is a rational number?
For what natural numbers \(a\) and \(b\) is the number \(\log_{a} b\) rational?