There isn't any option to view when someone accessed your computer but you can pull up Firefox history and see when someone accessed Gmail with a date/time.
In Firefox, press Cmd+Shift+H
I think you are referring to Mac Console
Go to Applications>Utilities>console.app
Here are what the options show and mean:
Clicking on "Show Log List" in the toolbar will bring up the Log List. The Log List opens a sidebar which shows all of the different logs that the system maintains. This list helps in viewing the many different logs maintained in various parts of the system by bringing them all together to one place. By clicking on a particular log category, all of the logs will be shown.
System Log Queries
The System Log Queries contains all of the logs that have to do with the entire system. This includes system logs as well as individual application logs.
Selecting All Messages gives a live look at your computer's activities, updated live. This includes all activities from both the system as well as any applications running. Logs in this section of the Console are all formatted uniformly. They all include a timestamp, the name of the process or application, and the actual message of the log. When the message displayed includes a paperclip icon next to it, it means that it is a shortened version of a longer report, and clicking the icon will show the complete report.
In addition to viewing all messages, users can also create custom queries with any criteria that they like. These custom queries will filter the messages and will also be shown in the All Messages section. In order to make a new query, choose "New System Log Query" from the File menu.
Diagnostic and usage information
Logs in this section include diagnostic events by either an application or the user. Diagnostic events include:
Diagnostic and Usage Messages
Messages in this section of the console mainly tell how the system or applications are used. The section contains only the messages, not the actual reports of the problem. While the system log shows ongoing activities of the system, the Diagnostic and Usage Messages section contains information about system hangs and application crashes.
User Diagnostic Reports
User Diagnostic Reports are messages that relate to the current user's account. Messages from programs that are running while they are logged in will be displayed in this section.
System Diagnostic Reports
System diagnostic reports include the following information:
Files are used to separate the log files into different categories for easier viewing. While all of the logs can be seen in the all messages section, logs in this section are organized based on the different criteria, and are also linked to the actual files. Therefore, in this section, a user can locate the log file they are looking in a finder window.
Logs found in this section all relate to drivers and kernel extensions that load when you boot. System.log may also contain drivers and software that are not used any longer, but have lingering services still running. Many times, hardware failures are the cause of drivers, and the log files for those can be found here as well. Most of the logs contained here are from events that occur when the system goes to sleep, shutdowns, restarts, or starts back up.
Logs found in this section are the result of the software communicating with the hardware. When a problem occurs in the translation of commands from the system or an application to the cpu and other electric components of a computer, the log that gets created is stored here.
The logs contained under these folders track the activity in the account of the current user who is logged in. By expanding the folder, you can find logs for specific programs and services within your account. Crash reporter logs are also located in this section. They contain information about applications when they crash, and they can be sent to developers in order to figure out the cause of a crash.
The logs contained here offer the same ability to expand folders and find logs for specific programs and services, however, they are the logs for anyone who uses the computer. This section contains the log files for both the user currently using the computer, as well as for any other accounts on the computer.
Logs in this section are mainly low level logs that do not contain information about any particular application or any specific part of the system. They contain authorization logs for using the system and various applications.
The logs will show when Firefox was opened but that does not help unless you know the exact date/time. You should use Firefox history -- It will show when Gmail.com was accessed if you can find the date/time; it could take a lot of scrolling and checking.
Whose email address was showing? It is something you recognize?
Correct -- The actual time an account logged into is something that can be found if you are sign into that Gmail account. For example, if you signed into that account, it would show the last 5 times the account was logged into (including the date/time and location)
I understand what you would like to know but it is not possible unless either you can access their account (sign into it) or you had a keylogger program installed on your computer that records the keystrokes.
The log will have when Firefox was opened and use and the Firefox history will show the history of Gmail.com being accessed.