# $$\frac{\ln b-\ln a}{b-a}$$

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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