Software logging is critical for system observability, yet developers face a dual crisis of costly overlogging and risky underlogging. Existing automated logging tools often overlook the fundamental whether-to-log decision and struggle with the composite nature of logging. In this paper, we propose Autologger, a novel hybrid framework that addresses the complete the end-to-end logging pipeline. Autologger first employs a fine-tuned classifier, the Judger, to accurately determine if a method requires new logging statements. If logging is needed, a multi-agent system is activated. The system includes specialized agents: a Locator dedicated to determining where to log, and a Generator focused on what to log. These agents work together, utilizing our designed program analysis and retrieval tools. We evaluate Autologger on a large corpus from three mature open-source projects against state-of-the-art baselines. Our results show that Autologger achieves 96.63% F1-score on the crucial whether-to-log decision. In an end-to-end setting, Autologger improves the overall quality of generated logging statements by 16.13% over the strongest baseline, as measured by an LLM-as-a-judge score. We also demonstrate that our framework is generalizable, consistently boosting the performance of various backbone LLMs.