For Android, please add the below to your Android manifest in the same tag where you added your AppLovin SDK key:
For iOS, please ad the following key-value to your .plist file: "AppLovinVerboseLoggingOn" set to "true". You can also see attached screenshot.
NOTE: If you are having trouble seeing the verbose logging. Make sure that you aren't initializing the SDK with an empty settings object. Also, for Xcode make sure that you have "All Output" selected at the bottom of your output console window.