Where can I find the logs for my Electron app in production?

If you mean console from within the webapp, then this applies :)

You need to make a callback for this to work. Read more about them here: http://electron.atom.io/docs/api/remote/

Here is a short example:

In a file next to your electron main.js, named logger.js, add this code:

exports.log = (entry) => {
    console.log(entry);
}

And then in your webapp, use this to call this log method callback:

// This line gets the code from the newly created file logger.js
const logger = require('electron').remote.require('./logger');

// This line calls the function exports.log from the logger.js file, but
// this happens in the context of the electron app, so from here you can 
// see it in the console when running the electron app or write to disk.
logger.log('Woohoo!');

You might also want to have a look at https://www.npmjs.com/package/electron-log for "better" logging and writing to disk. But you always need to use callbacks.