Prove by epsilon delta method that $f(x) = \log(x)$ is continuous at $x=2$ [duplicate]

I am confused, about how to proceed with this question, I got this far only and got stuck :For any $\varepsilon>0$, there exist $δ>0$ such that $$|\log(x) - \log(2)|<\varepsilon $$whenever$$\delta>|x-2|\implies \delta +2 > x > 2- \delta$$I pick $\delta = 1$, then$$3<x<5$$$$\log(3)<\log(x)<\log(5)$$$$\log(x/2) < \log(5/2)$$

I think it may be wrong too, please help.