# $$\ln \frac{\beta}{\alpha}$$

Calculus Level 2

For two real numbers $$a$$ and $$b$$ ($$a < b$$) in the closed interval $$[0,1],$$ if $\frac{e^{7b}-e^{7a}}{b-a}=k,$ the range of the constant $$k$$ can be expressed as $$\alpha < k < \beta.$$ What is the value of $$\ln \frac{\beta}{\alpha}?$$

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