Solving Exponential Inequality I would like to know the range of $n$ where this condition is true. Can somebody help me with it. The equation is as follows
$$n^{100}\le2^{n^2}$$

$$n^{100}\leq2^{n^2}$$
$$n\leq 2^{\frac{n^2}{100}}$$
right-hand side grows faster, so if it's true for a constant $c$, then it's true for every number greater than $c$. $c=21$ and thus the inequality holds true for:
$$n=1 \vee n\geq 21$$
