Log management is crucial for ensuring the security, integrity, and compliance of modern information systems. Traditional log management solutions face challenges in achieving tamper-proofing, scalability, and real-time processing in distributed environments. This paper presents a blockchain-based log management framework that addresses these limitations by leveraging blockchain's decentralized, immutable, and transparent features. The framework integrates a hybrid on-chain and off-chain storage model, combining blockchain's integrity guarantees with the scalability of distributed storage solutions like IPFS. Smart contracts automate log validation and access control, while cryptographic techniques ensure privacy and confidentiality. With a focus on real-time log processing, the framework is designed to handle the high-volume log generation typical in large-scale systems, such as data centers and network infrastructure. Performance evaluations demonstrate the framework's scalability, low latency, and ability to manage millions of log entries while maintaining strong security guarantees. Additionally, the paper discusses challenges like blockchain storage overhead and energy consumption, offering insights for enhancing future systems.