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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. 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