What is the limit as x approaches infinity of

Question

a)logx/log(2x) b)logx/log(x^2) I tried L'Hospital's Rule first but messed up along the the way? 

 

 

Answer 1

(a) Given function

L'Hopital's Rule :

 = 1

The solution is Lim [logx/log(2x)] = 1

 

Answer 2

(b)

Given function

L'Hopital's Rule :

 = 1/2

The solution is Lim [logx/log(x²)] = 1/2