Manipulation of Logarithms

Level pending

\[\begin{cases} \log(AB) = X \\ \log(A)\log(B) = Y \\ \log_{A}(B) - \log_{B}(A) = Z\end{cases} \]

Given the above, find the value of: \(\log(B) - \log(A)\) in terms of \(X\) and \(Y\) and \(Z\).