Jackson logarithm of a product
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Theorem
Let $\mathbb{T}$ be a time scale. The following formula holds: $$\log_{\mathbb{T}}(f(t)g(t))=\log_{\mathbb{T}} f(t) \oplus \log_{\mathbb{T}} g(t),$$ where $\log_{\mathbb{T}}$ denotes the Jackson logarithm and $\oplus$ denotes forward circle plus.
