Blockchains only make sense when you need to ensure the integrity of, well, a chain.
In the most general case, the way a blockchain works is that each block contains a data payload, and a verification hash, which is a fixed-size summary of
- The payload of this block, and
- The entirety of the preceding block.
Because the hash of the preceding block was based on the entirety of the block before that, and so on, the hash for any given block depends on the payloads of all previous blocks. That means it is very difficult to alter a block far back in the chain, because you would have to update every subsequent block as well. The older a block is, the harder it is to alter. However, newer blocks are easy to alter, and it is easy to produce alternate histories (essentially producing a block tree), and using a blockchain in an of itself is no defense against hacking. Blockchain applications (like, say, Bitcoin) thus all require some additional method of establishing concensus on what the most recent block is, because the security of a blockchain depends on age and there is no inherent protection on that most recent block. Additionally, a lot of the security of, e.g., Bitcoin, also depends on the distributed nature of the particular blockchain in use; if the data is spread over hundreds or thousands of different clients, it becomes completely impractical to alter the data on >50% of them; but if you are dealing with a localized log, it is much easier to rewrite a huge chunk of history to account for whatever changes you might want to make to a single old block.
So, if you want to ensure that nothing has been removed from old logs, then using a blockchain data structure might be one component of the security measures for your ship's log--but it would be stupid to make it the only security measure, and other approaches to data integrity make blockchain largely superfluous in those circumstances.