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System logs are essential for security monitoring and digital forensics, but they remain vulnerable to tampering when attackers gain elevated privileges. Existing logging systems often fail to guarantee integrity, allowing adversaries to alter or delete critical evidence. This paper presents a lightweight tamper-proof logging system that ensures log integrity using kernel-level event capture with eBPF, cryptographic hash chains, Merkle tree-based verification, and cloud-based integrity anchoring. The proposed system enables real-time log collection, efficient integrity validation, and reliable detection of unauthorized modifications without relying on blockchain or specialized hardware.