I think the linking info will - by default - appear in the cd_core.log, since this seems to be a "catch-all" log for all com.tridion.* classes.
You can add a log explicitly for linking as follows:
Create a linking-only appender:
<appender name="linkingLog" class="ch.qos.logback.core.rolling.RollingFileAppender">
<rollingPolicy class="ch.qos.logback.core.rolling.TimeBasedRollingPolicy">
<fileNamePattern>${log.folder}/cd_link.%d{yyyy-MM-dd}.log</fileNamePattern>
<maxHistory>${log.history}</maxHistory>
</rollingPolicy>
<encoder>
<pattern>${log.pattern}</pattern>
</encoder>
<prudent>true</prudent>
</appender>
Then bind the linking classes to this appender:
<logger name="com.tridion.linking" level="${log.level}">
<appender-ref ref="linkingLog"/>
</logger>
if you want to use a different log level for this specific log file, then change it in the logger element.