Skype does not automatically generate application and error logs. In fact, to access such logs, you will first need to download and configure logging software available from the Skype website. If it's conversation logs you're after, then you needn't look further than the Skype software itself.
Application Logs in Windows 8
Download the Skype logging software and unzip the package to any location on your computer. Open a "Run" prompt and enter the exact location of the command file contained within the unzipped folder, adding a space and the word "enable" after the file path. This command will launch Skype with the log application running. Your log files will be stored in the same directory as the command file.
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Application Logs in Windows 7
Download the Skype logging software for Windows 7 and unzip the package to any location on your computer. Double-click the "logging-on" registry file to enable Skype application logging. Log files will be stored in C:\Users<yourusername>\AppData\Roaming\Skype on your computer.
To access your conversation history with a contact, simply select that person from the contact list in Skype. Your instant messaging and SMS history will be displayed in the primary panel of Skype. If ever you need to backup your conversation logs, open C:\Users<yourusername>\AppData\Roaming\Skype and save the "main.db" file.