Cisco device will not send log messages to your terminal session by default. That means that you will see log messages in putty only if you are connected to console port but if you connect with telnet or SSH you will not get log messages. Here’s how to resolve this:
There are three types of logging: Console, Monitor and Buffer.
Console logging is seen if you connect to console port directly. Monitor logging is what you will se on your screen when you are connected to CLi in some other way. And the last is Buffer logging that means all the logs that are going into buffer memory to be viewed later in time. Every of the logging type has its own setting on which loggs will be registered.
There are this types of looging levels with their severity numbers where greather number means smaller severity case, from severity 1 to 7: