How can I solve the equation $$\lceil \log_{b}{1024} \rceil = n$$ where $n \in \mathbb{N}$ in terms of $b$? I have seen equations of a similar form (Solving an equation with floor function before), but I'm not sure how to proceed with this one.
2026-03-27 02:32:49.1774578769
Solving equation involving the ceiling function
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Hint. An equation involving the ceiling function is not "really" an equation, it is "really" an inequation: $$\lceil\log_b1024\rceil=n$$ means $$n-1<\log_b1024\le n\ .$$ If you are familiar with basic properties of logarithms and inequalities, you should not have any trouble completing the solution.