Question

prove prove 2^n>3n by induction

Answer 1

Check the question. If you put n=1 you get 2^n=2, which is not greater than 3n=3
Will it be 2^n<3n?

Answer 2

^^ check n=5

Answer 3

but yeah there is something missin from the question

Answer 4

it is true for all n >3
initial case:
2^4 > 3*4
16 > 12
let this be represented using k
2^k > 3k
for k+1
2^(k+1) > 3(k+1)
2*2^k > 3k +3
now assume 2^k = 3k which is an underestimate
--> 2*3k > 3k+3
-->6k > 3k+3 , this is true for all k>1 and since this is underestimate the premise must be true that :
2^k+1 = 3(k+1) for any k>3

Therefore 2^n > 3n, for all n>3