Forensic analysis of web server logs demands both accurate detection and human-readable explanations that can satisfy legal requirements. We present CEF-Log, a context-enhanced few-shot chain-of-thought prompting strategy for Large Language Models that addresses this dual requirement. CEF-Log embeds expert investigative methodology through a structured five-step reasoning template, enabling the model to learn \textit{how} to analyze logs rather than \textit{what} patterns to memorize. Experimental evaluation demonstrates that CEF-Log achieves an F1-score of 0.99 on the CSIC 2010 dataset using only four examples while providing a $10\times$ improvement in sample efficiency compared to other prompting-based methods. We also introduce ForenWebLog, a new dataset that incorporates real-world attacks and multi-step attack sequences for comprehensive evaluation. Qualitative analysis confirms that CEF-Log generates traceable, accurate explanations suitable for forensic documentation, addressing the critical "black-box" limitation of traditional machine learning approaches.