Is the Limit of 5^x/x as x Approaches Infinity Really Infinity?

[cue928]

Lim as n-> inf: 5^x/x
So I used l'hopital's rule and came up with (5^x)(ln(5))
As n becomes progressively larger, it is continually multiplied by ln(5) but the overall number still goes to infinity. Is that correct logic?

 

[SammyS]

There is no 'n' in your expression.

 

[cue928]

Sorry, replace the x's with n's. Skipped a step in my haste to type.

 

[abhip]

After you apply L Hospital for the first time u get 5^nln(5)/1 now write that expression as ln5/5^-n...this is a form of k/0 where k is a constant...this form will tend to infinity if k is positive else minus infinity