Bohner logarithm sub a product

Theorem

Let $\mathbb{T}$ be a time scale and let $p, q \colon \mathbb{T} \rightarrow \mathbb{C}$. The following formula holds: $$L_{pq}(t,s)=L_p(t,s)+L_q(t,s)+\displaystyle\int_s^t \dfrac{\mu(\tau)p^{\Delta}(\tau)q^{\Delta}(\tau)}{p(\tau)q(\tau)} \Delta \tau,$$ where $L_{pq}$ denotes the Bohner logarithm.