Hello! I am reading Schwarz book on QFT and I am at the renormalization group part. I understand the math and the fact that grouping terms perturbatively and requiring them to be 0, when taking the derivatives with respect to a given arbitrary chosen scale, allows perturbative corrections to the coupling constant as a function of momentum transfer. But I am not really sure I understand the large logarithms arguments. Why are they important? I don't really see them used in any of the proofs. You just take the derivative, set it to zero and you get what you want. Can someone explain to me what is the deal with large logarithms and why they seem to be so important in relation to the RG? Thank you!