Is this $2^{\lceil\log_2 d\rceil}$ inequality true?

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Is it true that $\frac{2^{t}-1}{t}+\frac d{t}>\frac d{\lceil\log_2 d\rceil}$ holds always for every large enough $d\in\mathbb N$ and $t\geq\lceil\log_2 d\rceil$?