Solving equation involving the ceiling function 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.

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.
