We address several problems in intelligent log management of distributed cloud computing applications and their machine learning solutions. Those problems concern various tasks on characterizing data center states from logs, as well as from related or other quantitative metrics (time series), such as anomaly and change detection, identification of baseline models, impact quantification of abnormalities, and classification of incidents. These are highly required jobs to be performed by today's enterprise-grade cloud management solutions. We describe several approaches and algorithms that are validated to be effective in an automated log analytics combined with analytics from time series perspectives. The paper introduces novel concepts, approaches, and algorithms for feasible log-plus-metric-based management of data center applications in the context of integration of relevant technology products in the market.