\(\frac{\ln b-\ln a}{b-a}\)

Calculus Level 2

For real numbers \(a\) and \(b\) (\(a<b)\) in the interval \([4,11],\) the range of the real number \(k\) such that \[\frac{\ln b-\ln a}{b-a}=k\] can be expressed as \(\alpha < k < \beta.\) What is \(\frac{1}{\alpha\beta}?\)

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