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In this paper we study braneworld cosmology when the bulk space is a charged black hole in de Sitter space (Topological
Reissner-Nordstr\"om de Sitter Space) in general dimension, then we compute leading order correction to the Friedmann equation that arise from logarithmic corrections to the entropy in the holographic-branworld cosmological framwork. Finally we consider the holographic entropy bounds in this senario, we show the entropy bounds are also modified by logarithmic term.
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