In or into?

Hi,

‘imprint sth on/onto one’s memory’ - here I’d use both interchangeably

‘burn sth into one’s memory’ - only ‘into’ seems right here

‘fix sth in/into one’s memory’ - I’m on the fence here. I think I used ‘in’ in the past but I might have let ‘into’ slip out on a few occasions

'log sth in to one's memory' - here I'd use in to

Thank you.