think of in + vestigate, where we look for traces or remains of something.
sounds like wastage which is the remains of something.
think of prestige... the historical monuments that are still there are a vestige
Think if Investigation. While investigating, one traces truth
sound like wastage....appendix in human beings is a wastage coz its of no use....hence VESTIGE
Vestige ... make it vestigial and compare it to journal. They both refer to a record or trace of something.