Big data management for logs in digital forensics focuses on efficiently handling, storing, and analyzing the massive volume of log data generated across diverse digital systems and networks. Research in this domain explores scalable log collection, indexing, and correlation methods using distributed computing frameworks such as Hadoop, Spark, and Elasticsearch. Key areas include the design of real-time forensic log analysis systems, anomaly detection through machine learning, and the use of graph-based analytics for event reconstruction. Other significant topics involve secure log storage using blockchain, privacy-preserving log sharing, provenance tracking, and automated evidence extraction from heterogeneous sources. Moreover, integrating big data analytics with cloud and IoT forensic platforms, developing intelligent log reduction techniques to eliminate redundancy, and ensuring the integrity and admissibility of log-based evidence are emerging as vital research challenges in digital forensic investigations.