Prove that 3^n>n^4 for all n in N , n>=8
The Attempt at a Solution
Base case: 3^8>8^4
Assume 3^n>n^4. Show 3^n+1>(n+1)^4
I tried a lot of approaches to get from the inductive hypothesis to what I want to show
It looks like I went too far
My other approach is this. It looks a little bit crazy, but I think it works
I will show that n^4+2*3^n grows faster than (n+1)^4 by using limits and loopitals rule.