Logarithmic slope of total transit depth

For $\delta =A+B(1-e^{-\tau })$ and $\tau \propto {\lambda }^{-p}$, the logarithmic slope is $-pB\tau e^{-\tau }/\delta$. The opaque planetary baseline generally dilutes the slope. In the optically thin limit, the atmospheric excess $\delta -A$ has logarithmic slope $-p$.