2. Let $K$ be the largest integer for which $n^{200}<5^{300}$. What is the value of $10 K$ ?
Solution
110

We may rewrite the inequality as $\left(n^{2}\right)^{100}<\left(5^{3}\right)^{100}=125^{100}$. It follows that $n^{2}<5^{3}=125$. The maximum integer value of $n$ is therefore 11 . Therefore $K=11$ and $10 K=110$.