Modeling user behavior from unstructured software log-trace data is critical in providing personalized service (e.g., cross-platform recommendation). Existing user modeling approaches cannot well handle the long-term temporal information in log data, or produce semantically meaningful results for interpreting user logs. To address these challenges, we propose a Log2Intent framework for interpretable user modeling in this paper. Log2Intent adopts a deep sequential modeling framework that contains a temporal encoder, a semantic encoder and a log action decoder, and it fully captures the long-term temporal information in user sessions. Moreover, to bridge the semantic gap between log-trace data and human language, a recurrent semantics memory unit (RSMU) is proposed to encode the annotation sentences from an auxiliary software tutorial dataset, and the output of RSMU is fed into the semantic encoder of Log2Intent. Comprehensive experiments on a real-world Photoshop log-trace dataset with an auxiliary Photoshop tutorial dataset demonstrate the effectiveness of the proposed Log2Intent framework over the state-of-the-art log-trace user modeling method in three different tasks, including log annotation retrieval, user interest detection and user next action prediction.