# Finding the limit

#### goody

##### New member
Hello everyone, I need to find this limit . What I tried is that
,
but clearly, 1/x diverges so I don't think it was very helpful.
Could someone help me what I need to do please?

#### Opalg

##### MHB Oldtimer
Staff member
Hello everyone, I need to find this limit View attachment 10284. What I tried is that
View attachment 10285,
but clearly, 1/x diverges so I don't think it was very helpful.
Could someone help me what I need to do please?
Having got as far as $$\displaystyle \large e^{\lim_{x\to0}\frac1x\log\left(\frac{1^{x+1} + 2^{x+1} + 4^{x+1}}7\right)}$$, you could write the limit as $$\displaystyle \lim_{x\to0}\frac{\log\left(\frac{1^{x+1} + 2^{x+1} + 4^{x+1}}7\right)}x$$ and use l'Hopital. (When you have found that limit, don't forget to take the exponential in order to get the answer.)