Manipulation of Logarithms

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

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

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