where is the oracle 12c logfile?
The alert log never has been under ORACLE_HOME/log. 

It is in $ORACLE_BASE/diag/rdbms/&lt;sid&gt;/&lt;sid&gt;/trace and is named alert_&lt;sid&gt;.log 

If you don't have $ORACLE_BASE, this typically is equivalent to $ORACLE_HOME/../../..

This is no different in 12c than it was in 11g (or 10g if I recall correctly).

You can also use the ADRCI tool: http://docs.oracle.com/database/121/SUTIL/adrci.htm#SUTIL1474