think of in + vestigate, where we look for traces or remains of something.
sounds like wastage which is the remains of something.
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
like vestigial organs are trace elements of evolution
Vestige ... make it vestigial and compare it to journal. They both refer to a record or trace of something.