Oracle EBS R12 Log File Location

- Startup/Shutdown Log files: $INST_TOP/logs/appl/admin/log

- Patch log: $APPL_TOP/admin/$SID/log

- Autoconfig log file:
Apps: $INST_TOP/apps/$CONTEXT_NAME/admin/log/$MMDDHHMM/adconfig.log
DB: $ORACLE_HOME/appsutil/log/$CONTEXT_NAME/<MMDDHHMM>/adconfig.log
$ORACLE_HOME/appsutil/log/$CONTEXT_NAME/<MMDDHHMM>/NetServiceHandler.log

- Concurrent log: $INST_TOP/apps/$CONTEXT_NAME/logs/appl/conc/log
- Apache, OC4J and OPMN:
 $LOG_HOME/ora/10.1.3/Apache
 $LOG_HOME/ora/10.1.3/j2ee
 $LOG_HOME/ora/10.1.3/opmn

- Alert Log File: $ORACLE_HOME/admin/$CONTEXT_NAME/bdump/alert_$SID.log
- Clone log:

Preclone log files in source instance
Apps: $INST_TOP/apps/$CONTEXT_NAME/admin/log/ (StageAppsTier_MMDDHHMM.log)
DB: $ORACLE_HOME/appsutil/log/$CONTEXT_NAME/(StageDBTier_MMDDHHMM.log)

Clone log files in target instance
Apps :  $INST_TOP/apps/$CONTEXT_NAME/admin/log/ApplyAppsTier_<time>.log
DB: $ORACLE_HOME/appsutil/log/$CONTEXT_NAME/ApplyDBTier_<time>.log

For more information check for following metalink documents.
How to find location of Install, Autoconfig, Patching , Clone and other logs in R12 [ID 804603.1]
Oracle Application Server Diagnostic Tools and Log Files in Applications Release 12 [ID 454178.1]