Log analysis is fundamental to modern software observability systems, playing a key role in improving system reliability. Recently, there has been a growing adoption of Large Language Models (LLMs) for log anomaly detection, due to their ability to learn complex patterns. In this work, we propose a model-agnostic framework that allows seamless plug-and-play integration of different LLMs, making it easy to experiment with and select the model that fits specific needs. These models are first fine-tuned on normal log data, learning their patterns. During inference, the model predicts the most probable next tokens based on the preceding context in each sequence. Anomaly detection is performed using Top-K predictions, where sequences are flagged as anomalous if the actual log entry does not appear among the K most probable next tokens, with K determined using the validation dataset. The proposed framework is evaluated on three widely-used benchmark datasets—HDFS, BGL, and Thunderbird—where it consistently achieves competitive results, outperforming state-of-the-art methods in multiple scenarios. These results highlight the effectiveness of LLM-based log analysis and the importance of flexibility when selecting models for specific operational contexts.