Finding lambda of Master Theorem
As you correctly noted, the case 1 of the Master theorem applies here. In other words, the case 1 applies if $f(n) = O(n^{\log_b a - \lambda})$ for some constant $\lambda &gt; 0$. 

Indeed, we will have to see if we can find some $\lambda &gt; 0$ so that in this case, $\log n = O(n^{\log_4 2 - \lambda}) = O(n^{1/2-\lambda})$. Easy, we can pick any $\lambda &lt; 1/2$. Finally, be careful what the Master theorem now tells you: the solution to the recurrence 

$$T(n) = \Theta(n^{\log_4 2}) = \Theta(n^{1/2}) = \Theta(\sqrt n).$$