I need to find the smallest integer $k>0$ such that the following inequality holds:
$$(1-\frac{1}{365})^k\le\frac{1}{2}$$
The answer is supposedly greater than $200$. How can I find $k$?
2026-04-26 00:34:09.1777163649
How to find the smallest integer $k > 0$ such that the following inequality holds
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Hint: $$k\log(1-\frac{1}{365}) \leq \log\frac12$$