Mobile logging libraries are essential tools for debugging and monitoring Android applications, yet their privacy implications remain largely unexplored. This paper presents the first large-scale empirical study of privacy risks in Android logging practices, analyzing 48,702 applications from Google Play to identify sensitive data leakage through third-party logging frameworks. Our findings indicate that while only 3.4% of applications use third-party logging, nearly half (49.3%) of logging-enabled apps exhibit privacy leaks, with three dominant libraries, such as Timber, SLF4J, and Firebase, accounting for 99.7% of violations. Analysis reveals that privacy leaks predominantly stem from indirect data flows (62.5%) with moderate complexity (2-4 statements), originating primarily from user-info sources, although user-input sources represent a substantial risk. Distinct logging patterns emerge across frameworks: SLF4J shows balanced log level distribution, Timber concentrates heavily on DEBUG levels (78.5%), and Firebase is dominated by Analytics Events (98.0%). Longitudinal analysis demonstrates improving privacy practices over time (68.2% of apps reduced leaks), though persistent vulnerabilities underscore the need for systematic protection measures. This study identifies logging-based privacy risks in Android applications and provides actionable insights for developers and library maintainers. It highlights the critical need for practitioners to address both user information and user input as significant privacy threats when using third-party logging frameworks in Android applications.