Prove that $4^n > n^4$by induction for $n\ge 5$ That is a simple question and I can't start a simple desenveloment.
Just $k=5$ we have $4^5 = 1024 > 5^4 = 625$
for $k+1$: $4^{k+1} > (k+1)^4\Rightarrow 4^k > (k+1)^4/4$
And How can i proceed after that?
Best,

Hint:
For $k \geq 5$ the following is true:
$$k\sqrt2 > k+1$$
As:
$$5(\sqrt2 -1)>5\times \frac25 =2> 1$$
We can show that $\sqrt2 -1 >\frac25$ as such:
$$\sqrt2>\frac75$$
Now as both $\sqrt2$ and $\frac75$ are bigger than zero, the inequality is persevered by squaring.
$$2=\frac{50}{25}>\frac{49}{25}$$
