Activity Log Sample with Firestore + Cloud Functions Trigger

index.js

const functions = require('firebase-functions');
const admin = require('firebase-admin');

const firestore = admin.firestore();

exports.activityLog = functions.firestore
  .document('privacy/{uid}').onWrite(snap => {
    const uid = context.params.uid;
    const settings = snap.data();

    settings['udpate_time'] =   
      admin.firestore.FieldValue.serverTimestamp();

    firestore.collection(
      `activity_log/${uid}/entries`
    ).add(settings);

Security Rule

match /activity_log/{uid} {
   allow create: if request.auth.uid == uid;   
   allow update: if false;
   allow delete: if false;
}