0.693??? RC Time constant

Ow ow, quit picking at me, I'm old and this was nearly fifty years ago. I looked at some the other info here and I can see that it must be Logarithmic. I wasn't really sure of what Ratchit was getting at until he said " The important point is that you do not think that the rise or decay of a RC circuit is logarithmic instead of exponential." I'm convinced that it had to be logarithmic and I don't remember how the math went, like I said at the beginning, I was impressed to see that some of our electronic constants carry over to other fields, but I was young and inexperienced, now it's old and forgetful, please forgive me.
Here's something I put together, for what it's worth.
Jeff