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The Root Cause Analysis for this issue would be that you might be using an older version of googleapis library which doesn’t have GoogleAuth as a constructor.
The TypeError GoogleAuth is not a constructor
can be resolved by updating the googleapis library to the latest version.
Please run the below command to update the googleapis to the latest version :
npm i googleapis@latest
For more information related on how to Set Up Cloud Logging for Node.js using , please refer to this documentation
Source:stackexchange.com