User activity logs are important pieces of evidence in digital forensic investigations. In cloud forensics, it is difficult to collect user activity logs due to the fact of virtualization technologies and the multitenancy environment, which can infringe upon user privacy when collecting logs. Furthermore, the computing paradigm is shifting from conventional cloud computing toward edge computing, employing the advances of 5G network technology. This change in the computing paradigm has also brought about new challenges for digital forensics. Edge nodes that are close to users are exposed to security threats, and the collection of logs with limited computing resources is difficult. Therefore, this study proposes a logging scheme that considers log segmentation and distributed storage to collect logs from distributed edge nodes and to protect log confidentiality by taking into account edge-cloud characteristics. This scheme protects the integrity of log data collected by a multi-index chain network. To demonstrate the performance of the proposed scheme, edge nodes with three different capacity types were used, and the proposed log-segmentation method performed 29.4% to 64.2% faster than the Cloud-Log Assuring-Secrecy Scheme (CLASS) using 2048 bit Rivest-Shamir-Adleman (RSA) in three types of edge nodes for log-confidentiality protection. The log segmentation of edge CLASS (eCLASS) reduced the log size to approximately 58% less than CLASS log encryption, and edge-node CPU usage was also reduced from 14% to 28%.