During the normal operation of a Cloud solution, no one pays attention to the logs except the system reliability engineers, who may periodically check them to ensure that the Cloud platform's performance conforms to the Service Level Agreements (SLA). However, the moment a component fails, or a customer complains about a breach of SLA, the importance of logs increases significantly. All departments, including management, customer support, and even the actual customer, may turn to logs to determine the cause and timeline of the issue and to find the party responsible for the issue. The party at fault may be motivated to tamper with the logs to hide their role. Given the number and volume of logs generated by the Cloud platforms, many tampering opportunities exist. We argue that the critical nature of logs calls for immutability and verification mechanism without the presence of a single trusted party.This paper proposes such a mechanism by describing a blockchain-based log system, called Logchain, which can be integrated with existing private and public blockchain solutions. Logchain uses the immutability feature of blockchain to provide a tamper-resistance storage platform for log storage. Additionally, we propose a hierarchical structure to combine the hash-binding of two blockchains to address blockchains' scalability issues. To validate the mechanism, we integrate Logchain into two different types of blockchains. We choose Ethereum as a public, permission-less blockchain and IBM Blockchain as a private, permission-based one. We show that the solution is scalable on both the private and public blockchains. Additionally, we perform the analysis of the cost of ownership for private and public blockchains implementations to help a reader selecting an implementation that would be applicable to their needs. The Logchain's scalability improvement on a blockchain is achieved without any alteration on the fundamental architecture of blockchains. As shown in this work, it can function on private and public blockchains and, therefore, can be a suitable alternative for organizations that need a secure, immutable log storage platform.