Analyzing database access logs is a key part of performance tuning, intrusion detection, benchmark development, and many other database administration tasks. Unfortunately, it is common for production databases to deal with millions or even more queries each day, so these logs must be summarized before they can be used. Designing an appropriate summary encoding requires trading off between conciseness and information content. For example: simple workload sampling may miss rare, but high impact queries. In this paper, we present LogR, a lossy log compression scheme suitable use for many automated log analytics tools, as well as for human inspection. We formalize and analyze the space/fidelity trade-off in the context of a broader family of "pattern" and "pattern mixture" log encodings to which LogR belongs. We show through a series of experiments that LogR compressed encodings can be created efficiently, come with provable information-theoretic bounds on their accuracy, and outperform state-of-art log summarization strategies.