Limit problem

1. The problem statement, all variables and given/known data

find the limit as n->oo of n(ln(n+10)-ln(n))

2. Relevant equations



3. The attempt at a solution

the answer is 10 this is also part of my exam review I am pretty lost on this one I tried using log rules to combine the terms tried getting it in form for L'H but I don't know what to do.

 

I think I just found the answer...I combined the ln terms so ln((n+10)/n)^n = L then I exponentiated both sides to give ((n+10)/n)^n= e^L then The limit of (1 + 10/n)^n = e^10 = e^L so taking the ln of both sides gives 10 = L (I know the limit of (1 + 10/n)^n = e^10 because it is a given formula on my formula sheet)

 

I keep getting the wrong answer with this method I do L'H from where you said and I get (n/(1+10)*(-1(1+10)/n^2)*-n^2 ...

 

finally got it thanks