Logs for Tomcat are typically going to be in C:\RSA\Tomcat7-AMIS\Logs. Note for each AMIS item there is a different Tomcat7 folder instance. In this case, refer to thecommons-daemon.<date>.log which will contain the current date in place of the word date.
The error is due to the version number change which causes the file to not be found, just as the log noted. When Java is updated on the Windows side, the update deletes the old Java folder contents. All that is left is the folder with a few empty sub folders. In this case the updated version is now jre1.8.0_51 as compared to jre1.8.0_45, as shown:
When Tomcat starts it looks for the Java Virtual Machine path defined in the Tomcat configuration and can no longer find the jvm.dll file it needs to start. The path started out as C:\Program Files\Java\jre1.8.0_45\bin\server\jvm.dll which causes the error during startup.
To resolve the issue simply change the path so it points to the updated Java directory and services should start without issues.
Right click the first Tomcat icon for the AMIS framework service, then click Configure...
Check the Java path details by going under C:\Program Files\Java\ and making note of the newer folder with the higher end number. In this case it's 51, but in the future it may be 52 or above.
Set the path under the Tomcat Config > Java.
Click Apply or OK.
Repeat steps 1 - 4 for any other AMIS Prime Tomcat services you have on the server such as for the Self-Service Portal or Help Desk Admin Portal currently.
Right click and stop/start each Tomcat instance. All services should now be running as expected.