Go to the bdump directory to run these shell commands

 Date and errors in alert.log

     cat al* | \
     awk 'BEGIN{buf=""}
          /[0-9]:[0-9][0-9]:[0-9]/{buf=$0}
          /ORA-/{print buf,$0}'

 Date of startups in the alert.log

     cat al* | \
     awk 'BEGIN{buf=""}
          /[0-9]:[0-9][0-9]:[0-9]/{buf=$0}
          /Starting ORACLE/{print buf,$0}'