According to Elena's blog post this should be configurable in logback.xml and should output a file of the format sync_audiencemanager.%d{yyyy-MM-dd}.log
There is more information in the online documentation (requires login).
<appender name="rollingAudiencemanagerLog" class="ch.qos.logback.core.rolling.RollingFileAppender">
<rollingPolicy class="ch.qos.logback.core.rolling.TimeBasedRollingPolicy">
<fileNamePattern>${log.folder}/sync_audiencemanager.%d{yyyy-MM-dd}.log</fileNamePattern>
<maxHistory>${log.history}</maxHistory>
</rollingPolicy>
<encoder>
<pattern>${log.pattern}</pattern>
</encoder>
<prudent>true</prudent>
</appender>
<logger name="com.tridion.marketingsolution">
<appender-ref ref="rollingAudiencemanagerLog"/>
</logger>
