proof verification - Prove using induction that $(2^n)+1=2$

I needed help proving this statement, this is what I have tried so far

Base case:

$n = 2$

$5 < 9$ $->$ $True$

Inductive step:

Assume that for some $k>=2$ , $(2^k)+1<3^k$ show that $P(k+1)$ holds

-> 2^(k+1) + 1
-> 2*(2^k) + 1
-> (1+1)*(2^k) + 1
-> 2^k + 2^k + 1
 <  2^k + 3^k

This is where I get stuck I am not sure where to go from there or how to manipulate that to get 3^(k+1)

Any help would be appreciated thank you