Note: The following description is valid for version 3.5 of Android Studio. It could be different for other Android Studio version.
In the bottom row of Android Studio there is a "Build" tab. Click on it and the "Build" view will open. Ensure that the "Build Output" tab in the top row of the "Build" view is selected. There can also be other tabs (like "Sync"). Normally a graphical representation is shown. In this case click the "Toggle view" button to switch to the "text mode".
Keep in mind that Android Studio always builds with the default logging settings from Gradle and therefore no additional logs are visible. You can extract the build error from this view. But when the R&D team needs the debug logs from Gradle, then you have to manually execute the Android build in the console (or "Terminal" view from Android Studio).