Log, floor and ceiling together will make you surrender!

Given that \(x\) is a random real number between 1 and 4 and \(y\) is a random real number between 1 and 9.

The expected value of: \(\lceil \log_{2}x \rceil- \lfloor\log_{3}y \rfloor\) can be expressed as \(\frac{m}{n}\) where \(m\) and \(n\) are positive and relatively coprime integers. Then, find the value of \(100m+n\).

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